Ph.D.: Indiana University, 1951

Married: Barbara West 1952

Children:

- Martha Stack 1953
- Elizabeth Conley 1957
- Janet Sucha 1963

- Assistant Professor of Mathematics, 1954-56
- Associate Professor of Mathematics, 1956-59
- Professor of Mathematics, 1959-1995
- Head of School of Mathematics, 1964-65
- Regents' Professor of Mathematics, 1969-

- Professor Emeritus of Mathematics, 1995-

- Ordinary and Partial Differential Equations
- Foundations of Thermodynamics and Continuum Mechanics

Offices held in professional societies

** Honors and Awards **
[ back to top ]

- Doctor of Science, University of Sussex, 1972
- G.D. Birkhoff Prize in Applied Mathematics, American Mathematical Society, 1973
- Distinguished Alumni Award, Indiana University, 1979
- Fellow, American Association for the Advancement of Science, 1980-
- Member, National Academy of Sciences, 1980-
- Member, American Academy of Arts and Sciences, 1984-
- Doctor of Science, University of Ferrara, 1992
- Doctor of Science, University of Padova, 1992
- Foreign member, Finnish Academy of Sciences, 1995

** Graduate degrees
supervised ** [ back to top ]

- Jerome Sather, 1963
- Sylvan Burgstahler, 19638
- Arie Gaalswyk, 1963
- Howell Wilson, 1964
- Richard Hager, 1967
- James Ross, 1969
- William Serbyn, 1971
- Manuel Ricou, 1983
- Kevin McLeod, 1984
- Henghui Zou, 1992
- Giovanni Leoni, 1995
- Xiaodong Zhu, 1997

** Post-doctoral positions
** [ back to top ]

- Princeton University, Fine Instructor of Mathematics, 1951
- Massachusetts Institute of Technology, C.L.E. Moore Instructor of Mathematics, 1952-54

** Visiting positions **
[ back to top ]

- Stanford University Lecturer, Summer 1961
- University of Chicago, Visiting Professor, Spring 1964, Spring 1975
- The Johns Hopkins University, Visiting Professor, Spring 1966
- University of Sussex, Visiting Professor, 1967-68, 1970, 1972
- Mittag-Leffler Institute, Stockholm, Visiting Professor, 1975
- University of Naples, Visiting Professor, Summer 1979
- University of Perugia, Visiting Professor, Spring 1985
- Oxford University, Visiting Professor, Spring 1986
- University of Modena, Visiting Professor, Spring 1988
- National Science Council Special Lectureship Program, Taiwan, ROC, September 1988
- Georgia Institute of Technology, Visiting Professor, Fall 1990
- University of Perugia, Visiting Professor, Summer 1992

** Editorial boards
** [ back to top ]

- Archive for Rational Mechanics and Analysis, 1963- (co-editor 1969-1986)
- Journal of Differential Equations, 1976-
- Communications in Partial Differential Equations, 1978-95
- Bulletin of the American Mathematical Society 1978-80
- Rendiconti Circolo Matematico di Palermo, 1980-
- Atti del Seminario Matematico, University of Modena, 1985-1998
- Asymptotic Analysis, 1988 -1998
- Differential and Integral Equations, 1989 -
- Communications in Applied Analysis, 1995 -
- Advances in Differential Equations, 1995 -
- Electronic Journal of Differential Equations, 1995 -

** Invited addresses **
[ back to top ]

- Invited hour lecture, American Mathematical Society, Evanston, 1964
- Special session on Differentiation Theory, American Mathematical Society, Evanston, 1968
- Special session on Partial Differential Equations, American Mathematical Society, Ann Arbor, 1969
- International Congress of Mathematicians, Nice, 1970
- Summer Institute on Partial Differential Equations, American
Mathematical Society, Berkeley, 1971 (organizing committee; 3 lectures) - British Theoretical Mechanics Colloquium, University College, London, 1972
- Convegno Internazionale sul Metodi Valutativi nella Fisica-Matematica, Accademia Nazionale dei Lincei, Rome, 1972
- Birkhoff Session, American Mathematical Society, Dallas, 1973
- Invited hour lecture, Hilbert Anniversary Symposium, American Mathematical Society, DeKalb, Illinois, 1974
- Society for Natural Philosophy, Scuola Normale Superieure di Pisa, 1974
- Swedish Mathematical Society, Linkoping, Sweden, 1975
- Finnish Mathematical Society, Helsinki, Finland, 1975
- Conference on Ordinary and Partial Differential Equations, Dundee, 1976 (2 lectures)
- Southwest Mechanics Lecture Series; New Orleans, Houston, Austin, 1976 (4 lectures)
- NSF-CBMS Regional Summer Conference; Ball State University, 1978 (10 lectures)
- Special session on Conceptual Analysis in Thermodynamics, American Mathematical Society, Providence, 1978
- Third Annual Bateman Lectures; Johns Hopkins University., 1978
- International Society for the Interaction of Mathematics and Mechanics, Edinburgh, 1979
- American Mathematical Society, Kent State University, Ohio, 1979
- SAFA conference, Naples, Italy, March 21-28, 1980 (3 lectures)
- Society for Natural Philosophy, Rolla, Missouri, November 10, 1980
- Cortona (CIME) Summer lecture series, August 1981 (20 lectures)
- University of Washington, Pullman, March 1982. Three lectures on the foundations of thermodynamics.
- Cortona (CIME) Summer series, May 1982 (5 lectures)
- Varenna (CIME) Summer lecture series, September 1982 (8 lectures)
- International Congress of Mathematicians, August, 1983
- Italian Mathematical Union, September, 1983
- Society for Natural Philosophy, Brown University, November, 1983
- Special Sesion on Differential Equations, American Mathematical Society, Notre Dame, April 1984
- Commonwealth lectures on Applied Mathematics, Department of Mathematics, University of Massachusetts, Amherst, May 2-4, 1984 (3 lectures)
- Centenary of the Circolo Mathematico di Palermo, October 1984
- Distinguished Lecture Series, University of Southern California, November 1984
- Lecture Series in Applications of Mathematics, University of Southern California, Los Angeles, November 1984.
- Special Session on Mathematical Physics and Thermodynamics, American Mathematical Society, San Diego State University, November 1984
- Society for Natural Philsophy, University of Wisconsin, November 1984.
- Convegno celebrativo del centenario della nascita di Mauro Picone e di Leonida Tonelli. Accademia nazionale dei Lincei, Rome, May 1985
- Nineteenth Midwestern Mechanics Conference, Ohio State
- University, September 1985 North British Differential Equations Seminar, University of Edinburgh (2 lectures), April 1986.
- Convegno in onore di Hans Lewy, Universita di Trento, June, 1986.
- Conference on Nonlinear Partial Differential Equations, Brigham Young University, March 1987
- Lecture Series "Science and Pseudo Science" sponsored by the Chemical Engineering Department, University of Minnesota, February 1987
- Third Gregynog Symposium on Differential Equations, University College of Wales, July 1987
- Conference on Nonlinear Differential Equations, University of Leiden, October 13, 1987. "The structure of solutions of Lane-Enden type equations".
- Special Session on Nonlinear Differential Equations, Annual meeting, Canadian Mathematical Society, Vancouver, December 14, 1987. "The structure of radial solutions of the nonlinear p-Laplace equation".
- Conference on semilinear diffusion equations, University of Leiden, October 1987
- Special session on differential equations, Annual Meeting Canadian Mathematical Society, Vancouver, December 1987.
- Conference on foundations of thermodynamics, University of Valencia, September 1987
- Conference on modern developments in natural philosophy, Society for Natural Philosophy, The Johns Hopkins University, March 1988.
- Ontario Mathematical Society, Spring meeting, Waterloo, Ontario, April, 1988
- Conference in memory of Guido Stampacchia, Rome, April, 1988
- Conference on geometric methods in partial differential equations, Cortona, Italy, June 1988.
- Conference on Partial Differential Equations, Academy of Sciences, Torino, October, 1988
- Society for Natural Philosophy, University of Pisa, May 1989
- Conference in honor of David Gilbarg, Stanford University, June 1989
- Special session on Differential Equations, American Mathematical Society, Muncie, October 1989
- Georgia Institute of Technology, October 1989
- Weizmann Institute of Science, Rehovot, March, 1990
- St. Anthony Falls Hydraulics Laboratory, November 1989
- Princeton University, November 1989
- Binational workshop on Optimization and Nonlinear Analysis, The Technion, Haifa, Israel, March, 1990.
- Conference on Recent Development in Mechanics, Society for Natural Philosophy, University of Nebraska, April 1990
- Conference on Nonlinear Analysis and Partial Differential Equations in honor of Felix Browder, Rutgers University, May 1990
- Conference on Boundary Value Problems for Ordinary Differential Equations, Ohio University, June 1990.
- Conference on Fluid Mechanics and Partial Differential Equations, University of Ferrara, October 1990.
- Conference on "Nonlinear Waves" in honor of F.V. Atkinson, University of Ottawa, April 6, 1991.
- Conference on Advances in Modern Continuum Dynamics, Isola d'Elba, Italy, June 11, 1991
- Conference on New Developments in Partial Differential Equations, University of Ferrara, October 15, 1991
- Conference in Memory of Lambert Cesari, Academia della Scienze di Modena, October 25, 1991
- Conference on Differential Equations and Mathematical Physics, Georgia Institute of Technology, March 1992
- International Conference on Partial Differential Equations in honor of Luigi Amerio, Polytechnic University of Milan, September, 1992
- Conference on Partial Differential Equations of Elliptic Type, Cortona, October, 1992.
- Lectio Doctoralis, University of Ferrara, October 1992.
- Lectio Doctoralis, University of Padova, December 1992.
- Conference on Differential Equation and Continuum Mechanics, Stanford University, August, 1993
- Differential Equations Conference, Ohio University, Athens, Ohio, August, 1993
- Third Dublin Conference on Differential Equations, Dublin City University, September 1993
- Conference in Memory of Ilya Bakelman, Texas A&M Univesity, October, 1993
- Conference on Nonlinear Analysis, Krakov University, July, 1994
- Conference on Thermodynamics and Continuum Mechanics, University of Rome II, July 1994
- Thermoelastic Problems and the Thermodynamics of Continua, American Society of Mechanical Engineers, University of California, Los Angeles, June, 1995.
- N.M. Riviere Memorial Lecture, University of Minnesota, May 1995
- Fifth colloquim on qualitative theory of differential equations, Bolyai Institute, Szeged, Hungary, August, 1996
- International conference on nonlinear differential equations and applications. Golden Jubilee Year Tata Institute for Fundamental Research, Bongalore, August, 1996
- Conference in honor of Calogero Vinti, University of Perugia, October 1996
- Conference on the 20th Anniversary of International Journal of Mathematics and Mathematical Sciences, Univ. of Central Florida, March, 1997
- Conference on Nonlinear Problems in Science and Engineering, Indiana University, June, 1997
- International conference on Differential Equations and Dynamical Systems, University of Waterloo, Canada, August, 1997
- Conference in honor of Olga Oleinik, Iowa State University, November, 1997
- International workshop of differential equations and applications, Technion, Haifa, Israel, December, 1997
- Conference in honor of L.A. Peletier, Paris, March, 1998
- Functional Analysis and Nonlinear Partial Differential Equations, Delft, May, 1998
- Workshop on Nonlinear Differential Equations, University of Campinas, Brazil, August, 1998
- Conference in honor of Olga Ladyzhenshaya, Iowa State University, Ames, Iowa, August, 1998

**Invited symposia ** [ back to top ]

- International Symposium on Partial Differential Equations and the Geometry of Normed Spaces, Jerusalem, 1972
- North British Partial Differential Equations Year, Newcastle University, 1972 (3 lectures)
- Biannual symposium on Fluid Mechanics, Polish Academy of Sciences, Bialowiecza, Poland, 1975
- Mathematical Association of America, North Central Section, 1976
- Midwest Partial Differential Equations Seminar; Evanston, Ill., 1977
- International Symposium in Mechanics and Partial Differential Equations; Rio de Janeiro, 1977
- United States - Italian Science Program; Venice, 1978
- Society for Engineering Science, Northwestern University, 1979
- Goffman Symposium on Analysis, Purdue University, 1979
- Cesari Retirement Symposium, University of Michigan, September 25, 1980
- Symposium for Lamberto Cesari, Universita di Bologna, May 3, 1982
- Workshop on Foundations of Thermodynamics and Phase Transitions, Institute for Mathematics and its Applications, University of Minnesota, June 6-10, 1983
- Symposium for Carlo Miranda, University of Naples, September, 1982
- Texas A & M University, April 1983. (4 lectures)
- Mathematics Research Center Conference, University of Wisconsin, October, 1983
- Mechanical engineering lecture series, Northern Michigan University, December, 1983
- Midwest Partial Differential Equations Conference, University of Chicago, April 28, 1984
- Conference on Fluid Mechanics, University of Pisa, May 1987
- Conference on Thermodynamics, University of Valencia, October 2, 1987. "The Navier-Stokes equations with weak first law thermodynamics".
- Lecture Series for Thermodynamics Year, Politecnico di Torino, October 1987
- International Centre for Theoretical Physics, Trieste, September 1990.
- Vito Volterra lecturer, University of Rome II, December 1992 (3 lectures)
- Mathematical Aspects of Continuum Mechanics, in honor of Walter Noll. Society for Natural Philosophy, Pittsburgh, April 1993.
- Workshop on Energy Methods, Oviedo, Spain, March 1994
- Conference on Differential Inclusions and Stability, University of Perugia, March, 1994
- Southeastern-Atlantic Regional Conference on Differential Equations, University of Tennessee, October 1994
- Qualitative Aspects of Partial Differential Equations, Oberwolfach, Germany, February, 1995.
- Reaction-Diffusion Systems, University of Trieste, October, 1995.
- Waves and Stability in Continuous Media, Palermo, October, 1995
- Southern California Partial Differential Equations Conference, University of California, Riverside, November, 1995
- Recent trends in elliptic equations and related topics, Santander, Spain, July 1996 (3 lectures)

** Offices held in professional societies
** [ back to top ]

- President, Society for Natural Philosophy, 1969-70
- Council, American Mathematical Society, 1972-74

- Editorial Committee for the Research Expository Journal, American Mathematical Society 1976-1980
- Chairman, Committee on Prizes, American Mathematical Society, 1977
- Committee to Select the Winner of the Birkhoff Prize in Applied Mathematics, 1977
- Member, Scientific Advisory Council of the Mathematical Sciences Research Institute at the University of California, Berkeley, 1983-86
- Member, Committee on Resources for the Mathematical Sciences of the National Research Council (David Committee, 1984)
- Graduate Fellowship Evaluation Panel, National Research Council, 1983-84.
- Member, Oversight Committee, Theoretical Physics Institute, University of Minnesota, 1987
- Chairman, editorial committee for "Nonlinear Diffusion Equations and their Equilibrium States", MSRI Publications, Volumes 12 and 13, Springer- Verlag, 1988.
- Chairman, Organizing committee for Conference on Nonlinear Diffusion Equations and their Equilibrium States. August, 1989.
- Member, Progress in Mathematics Committee, American Mathematical Society, 1992-1995. Chair 1994-1995.

- Free boundaries and jets in the theory of cavitation, (with David Gilbarg). Journal of Mathematics and Physics, vol. 29 (1950), pp. 1-12.
- Uniqueness theorems for two free boundary problems. American Journal of Mathematics, vol. 74 (1952), pp. 492-506.
- Existence theorems for some hydrodynamical free boundary problems. Journal of Rational Mechanics and Analysis, vol. 1 (1952), pp. 1-48.
- Two hydrodynamical comparison theorems. Journal of Rational Mechanics and Analysis, vol. 1 (1952), pp. 563-572.
- Notes on hydrodynamics. Photoprinted by Princeton University under Office of Naval Research contract, (1952), 218 pages.
- On plane and axially symmetric free boundary problems. Journal of Rational Mechanics and Analysis, vol. 2 (1953), pp. 563-575.
- A note on the wave equation. Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 307-308.
- Comparison theorem for subsonic flows. Journal of Mathematics and Physics; vol. 23, pp. 27-45.
- On the Phragmen-Lindelo"f theorem for elliptic partial differential equations. Journal of Rational Mechanics and Analysis, vol. 3 (1954), pp. 395-413.
- A uniqueness theorem for the parabolic equation . Bulletin of the American Mathematical Society, vol. 60 (1954), p. 344.
- Uniqueness of axially symmetric subsonic flow past a finite body (with David Gilbarg). Journal of Rational Mechanics and Analysis, vol. 4 (1955), pp. 169-175.
- A characterization of regular boundary points for second order linear differential equations. Bulletin of the American Mathematical Society, vol. 61 (1955), p. 224.
- On the Harnack inequality for linear elliptic equations. Journal d'Analyse Mathematique, vol. 4 (1956), pp. 292-308.
- On isolated singularities of solutions of second order linear elliptic equations (with David Gilbarg). Journal d'Analyse Mathematique, vol. 4 (1956), pp. 309-340.
- A note on harmonic functions defined in a half-plane. Duke Mathematical Journal, vol. 24 (1956), pp. 523-526.
- On the Holder continuity of quasi-conformal and elliptic mappings (with R. Finn). Transactions of the American Mathematical Society, vol. 89 (1958), pp. 1-15.
- Mathematical principles of classical fluid mechanics. (Monograph) In Handbuch der Physik, vol. VIII/1 (1959), pp. 125-263. Russian translation: Foreign Literature Publishing House, Moscow 1963 (265 pages).
- On the stability of viscous fluid motion. Archive for Rational Mechanics and Analysis, vol. 3 (1959), pp. 1-13.
- A note on the existence of periodic solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, vol. 3 (1959), pp. 120-122.
- On the uniqueness of compressible fluid motions. Archive for Rational Mechanics and Analysis, vol. 3 (1959), pp. 271-288.
- On the derivation of stress-deformation relations for a Stokesian fluid. Journal of Mathematics and Mechanics, vol. 8 (1959), pp. 459-470.
- Poiseuille and Couette flow of non-Newtonian fluids. Zeitschrift for Angewandte Mathematik und Mechanik, vol. 39 (1959), pp. 295-299.
- On a fundamental theorem of the calculus of variations. Acta Mathematica, vol. 102 (1959), pp. 1-22.
- A new definition of the integral for non-parametric problems in the calculus of variations. Acta Mathematica, vol. 102 (1959), pp. 23-32.
- The exterior Dirichlet problem for second order elliptic equations (with Norman Meyers). Journal of Mathematics and Mechanics, vol. 9 (1960), pp. 513-538.
- On the area of curved surfaces. American Mathematical Monthly, vol. 68 (1961), pp. 435-440.
- On the differentiability of functions of several variables. Archive for Rational Mechanics and Analysis, vol. 7 (1961), pp. 359-372.
- On the definition and properties of certain variational integrals. Transactions of the American Mathematical Society, vol. 101 (1961), pp. 139-167.
- On the entropy change through a shock layer (with Y.C. Whang). Journal of Aerospace Sciences, vol. 28 (1961), pp. 990-991.
- Dirichlet's principle in the calculus of variations. Proceedings of Symposia in Pure Mathematics, vol. IV, pp. 17-22, Providence, 1961.
- Interior estimates for solutions of the Navier-Stokes equations. In "Partial Differential Equations and Continuum Mechanics", edited by R. Langer, pp. 376-378, University of Wisconsin Press, 1961.
- On the interior regularity of weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, vol. 9 (1962), pp. 187-195.
- Strong convergence in a product space. Proceedings of the American Mathematical Society, vol. 13 (1962), pp. 651-655.
- The initial value problem for the Navier-Stokes equations. In "Nonlinear problems", edited by R.E. Langer, pp. 69-98, University of Wisconsin Press, Madison, 1963.
- Variational problems of minimal surface type, I (with Howard Jenkins): Archive for Rational Mechanics and Analysis, vol. 12 (1963), pp. 185-212.
- A Harnack inequality for non-linear equations. Bulletin of the American Mathematical Society, vol. 69 (1963), pp. 481-486.
- Comparison and averaging methods in mathematical physics. Department of Mathematics, University of Minnesota, 1963. Also CIME publication, Rome Istituto Mat. dell'Universita, Edizioni Cremonese, 1965, 87 pages.
- A priori estimates for solutions of the minimal surface equation. Archive for Rational Mechanics and Analysis, vol. 14 (1963), pp. 376-383.
- Mathematical Aspects of Boundary Layer Theory, notes taken by H.K. Wilson, Department of Mathematics, University of Minnesota, Minneapolis 1963 (131 pages, multiplied typescript).
- Sublinear functions of measures and variational integrals (with C. Goffman), Duke Mathematical Journal, vol. 31 (1964), pp. 159-178.
- Local behavior of solutions of quasi-linear equations. Acta Mathematica, vol. III (1964), pp. 247-302.
- H = W (with Norman Meyers). Proceedings of the National Academy of Sciences, vol. 51 (1964), pp. 1055-1056.
- Removable singularities of solutions of elliptic equations. Archive for Rational Mechanics and Analysis, vol. 17 (1964), pp. 67-78.
- Pathological solutions of elliptic differential equations. Annali Scuola Normale Superiere di Pisa, Sci. Fis. Math., vol. 18 (1964), pp. 385-387.
- Singularities of solutions of nonlinear equations. Proceedings of Symposia in Pure Mathematics, vol. 17, pp. 68-88. Providence, 1965.
- Isolated singularities of solutions of quasi-linear equations. Acta Mathematica, vol. 113 (1965), pp. 219-240.
- Theory of differentiation. Department of Mathematics, University of Minnesota, 1965, 135 pages.
- Removable singularities of solutions of elliptic differential Equations, II. Archive for Rational Mechanics and Analysis, vol. 20 (1965), pp. 163-169.
- The Dirichlet problem for the minimal surface equation with infinite data (with Howard Jenkins). Bulletin of the American Mathematical Society, vol. 72 (1966), pp. 102-106.
- Variational problems of minimal surface type, II: Boundary value problems for the minimal surface equation (with Howard Jenkins). Archive for Rational Mechanics and Analysis, vol. 21 (1966), pp. 321-342.
- Isolated singularities of solutions of linear elliptic equations (with H. Weinberger). American Journal of Mathematics, vol. 88 (1966), pp. 258-272.
- Local behavior of solutions of quasi-linear parabolic equations (with D.G. Aronson). Archive for Rational Mechanics and Analysis, vol. 25 (1967), pp. 81-122.
- A maximum principle for nonlinear parabolic equations (with D.G. Aronson). Annali Scuola Normale Superieure di Pisa, Sci. Fis. Mat., vol. 21 (1967), pp. 291-305.
- The Dirichlet problem for quasi-linear elliptic equations with many independent variables. Proceedings of the National Academy of Science, vol. 58 (1967), pp. 1829-1835.
- On the non-existence of solutions of the Dirichlet problem for quasi-linear elliptic equations. Notices of the American Mathematical Society, vol. 14, (1967), p. 841.
- On the asymptotic behavior of velocity profiles in the Prandtl boundary layer theory. Proceedings of the Royal Society, Series A, vol. 299 (1967), pp. 491-507.
- The Dirichlet problem for the minimal surface equation in higher dimensions (with H. Jenkins). Journal fur die reine und angewandte Mathematik, vol. 223 (1968), pp. 170-187.
- Addendum to "A priori estimates for solutions of the minimal surface equation". Archive for Rational Mechanics and Analysis, vol. 28 (1968), pp. 149-154.
- On the mathematical basis of Prandtl's boundary layer theory: an example. Archive for Rational Mechanics and Analysis, vol. 28 (1968). pp. 217-225.
- Variational problems of minimal surface type, III: The Dirichlet problem with infinite data (with Howard Jenkins). Archive for Rational Mechanics and Analysis, vol. 29 (1968), pp. 304-322.
- The behavior of similar solutions in a compressible boundary layer (with J.B. McLeod). Journal of Fluid Mechanics, 34 (1968), pp. 337-342.
- A new proof in differentiation theory. Notices of the American Mathematical Society, vol. 15 (1968), p. 1036. Abstract. See also Rudin, W.: Real and Complex Analysis, Second Edition (McGraw-Hill, 1974), pp. xii and 435, and pp. 162-167.
- A general chain rule for derivatives and the change of variables formula for the Lebesgue integral (with D.E. Varberg). American Mathematical Monthly, vol. 76 (1969), pp. 514-520.
- The existence of similar solutions for some laminar boundary layer problems, (with J.B. McLeod). Archive for Rational Mechanics and Analysis, vol. 31 (1969), pp. 288-303.
- The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Philosophical Transactions of the Royal Society, vol. A264 (1969), pp. 413-496.
- On surfaces of constant mean curvature which span a given space curve. Mathematische Zeitschrift, vol. 88 (1969), pp. 77-88.
- Existence theorems for some compressible boundary layer problems. Proc. of the Conference on Qualitative Theory of Nonlinear Differential and Integral Equations, SIAM studies in Applied Mathematics, vol. 5 (1970), pp. 35-42.
- The Dirichlet problem for surfaces of constant mean curvature, Proceedings of the London Mathematical Society, vol. 21 (1970), pp. 361-384.
- On the strong maximum principle for nonlinear second order differential inequalities. Journal of Functional Analysis, vol. 5 (1970), pp. 184-193.
- Recent developments in the mathematical aspects of boundary layer theory. International Journal of Engineering Sciences, vol. 9 (1971), pp. 233-240.
- Uniqueness and comparison theorems for nonlinear elliptic equations in divergence form (with Jim Douglas, Jr., and Todd Dupont). Archive for Rational Mechanics and Analysis, vol. 42 (1971), pp. 157-168.
- The swirling vortex. Philosophical Transactions of the Royal Society of London, vol. 271 (1972), pp. 325-360.
- Boundary curvatures and the solvability of Dirichlet's Problem. Proceedings of the International congress of Mathematicians, vol. 2, (1970), pp. 867-875.
- A symmetry problem in potential theory. Archive for Rational Mechanics and Analysis, vol. 43 (1971), pp. 304-318.
- Gradient estimates for solutions of nonlinear elliptic and parabolic equations, In "Contributions to Nonlinear Functional Analysis", edited by E. Zarantonello, pp. 565-601, Univ. of Wisconsin Press, Madison, 1971.
- Nonlinear elliptic equations of second order. Lectures at Symposium on Partial Differential Equations, Berkeley, 1971. Mimeographed notes, 57 pages.
- Entire solutions of nonlinear Poisson equations. Proceedings London Mathematical Society, vol. 24 (1972), pp. 348-366.
- A note on the preceding paper of Amann. Archive for Rational Mechanics and Analysis, vol. 44 (1972), pp. 182-186.
- Rectilinear steady flow of simple fluids (with R.L. Fosdick). Proceedings Royal Society London, vol. 332 (1973), pp. 311-333.
- Liouville Theorems for nonlinear Poisson equations. Proceedings of the Convegno Internazionale sul Metodi Valutativi nella Fisica-Matematica, Rome, Accademia Lincei, 1975, pp. 207-215.
- Doomsday: on target? Science Magazine, vol. 189, (1975), pp 86-87.
- Global properties of continuum thermodynamic processes (with R.L. Fosdick). Archive for Rational Mechanics and Analysis, vol. 59 (1975), pp. 97-109.
- Foundations of classical thermodynamics. Lecture Notes, Department of Mathematics, University of Chicago, 1975. 223 pages.
- Curvature inequalities for surfaces over a disk (with H.F. Weinberger). In "Some problems of Mathematics and Mechanics" (M.A. Lavrentieff Anniversary Volume, edited by the Siberian Branch of the Akademia Nauk USSR), pp. 242- 250. English version: American Mathematical Society Translation 104 (1976), pp. 223-231.
- The solvability of boundary value problems: Hilbert's Twentieth Problem. In "Mathematical Developments Arising from Hilbert Problems", Proc. Symp. Pure Math., vol. 28, American Mathematical Society, Providence, 1976; pp. 507-524.
- Liouville theorems and gradient bounds for quasilinear elliptic systems. Arch. Rational Mech. Anal. 66 (1977), pp. 295-310.
- Optimal shapes for brittle beams under torsion (with H.F. Weinberger). In "Complex Analysis and its Applications", Steklov Institute (Acad. of Sciences) Jubilee Volume for I.Y. Vekua. Nauka Moscow 1978, pp. 88-91.
- Gradient estimates and Liouville theorems for quasilinear elliptic equations (with L.A. Peletier). Annali della Scuola Normale Superiore, Pisa, 5 (Series IV), 1978, pp. 65-104.
- The concepts of thermodynamics. In "Proc. Int. Symp. on Continuum Mechanics and Partial Differential Equations". North Holland Publishing Co., 1978, pp. 411-451.
- On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids (with R.L. Fosdick). Journal of Elasticity 9 (1979), pp. 83-89.
- Conceptual analysis of the classical second laws of thermodynamics. Archive for Rational Mechanics and Analysis, 70 (1979), 254-272.
- The foundations of thermodynamics. Gaz. Math. de Univ. Montreal, IV, No. 4 (1979), pp. 3-12.
- Foundations of thermodynamics, Lecture Notes, University of Naples, 1979. (150 pages).
- Phase transitions and interfacial layers for van der Waals fluids. In "Recent Methods in Nonlinear Analysis and Applications", Proceedings of the Fourth International Meeting of SAFA, eds. A. Canfora et al (Liguori Editore, Naples, Italy), pp. 169-175.
- The second law of thermodynamics for systems with approximate cycles (with Bernard D. Coleman and David R. Owen), Archive for Rational Mechanics and Analysis, 77 (1981), pp. 103-142.
- Uniqueness of solutions of semilinear Poisson equations (with K. McLeod). Proc. Natl. Acad. Sciences USA, 78 (1981), pp. 6592-6598.
- The form of interfacial surfaces in Korteweg's theory of phase equilibria. Quarterly of Applied Mathematics, 41 (1983), pp. 357-364.
- The mechanical theory of fluid interfaces and Maxwell's rule (with E. Aifantis). J. Coll. Interface Sci., 96 (1983), pp. 519-529.
- Equilibrium solutions in the mechanical theory of fluid microstructures (with E. Aifantis). J. Coll. Interface Sci., 96 (1983), pp. 530-547.
- The structure and laws of thermodynamics. Proc. International Congress of Mathematicians, Warsaw 1983, pp. 1717-1728.
- Uniqueness of positive solutions of semilinear equations in (with L.A. Peletier). Archive for Rational Mechanics and Analysis 81 (1983), pp. 181-197.
- Applied mathematics and scientific thought. In "Nonlinear Anaysis and Optimization", Lecture Notes in Mathematics, vol. 1107 (1984), pp. 19-27.
- Extensions of the mountain pass theorem (with P. Pucci). Journal of Functional Analysis, 59 (1984), pp. 185-210.
- One-dimensional shock layers in Korteweg Fluids (with R. Hagan). In "Phase Transformations and Material Instabilities in Solids", Academic Press, 1984, pp. 113-128.
- On the thermomechanics of interstitial working (with J.E. Dunn). Arch. Rational Mech. Anal. 88 (1985), pp. 95-133.
- A continuum model for chemical mixture dynamics. Proc. Nineteenth Midwestern Mechanics Conference. Columbus, Ohio (1985) pp. 59-64.
- Non-existence theorems for quasilinear partial differential equations (with W.-M. Ni). Supplemento di Rendiconti Circolo Matematico di Palermo, 8 (1985), pp. 171-185.
- Esistenza e unicita degli stati fondamentali per equazioni ellittiche quasilineare (with B. Franchi and E. Lanconelli). Rome, Rendiconti Acc. Naz. dei Lincei, Series 8, 79 (1985), pp 121-126.
- A mountain pass theorem (with P. Pucci). Journal of Differential Equations, 60 (1985), pp. 142-149.
- An outline of thermodynamical structure. In "New Perspectives in Thermodynamics", edited by J. Serrin, Springer-Verlag, 1986, pp. 3-32.
- Dynamic changes of phase in a van der Waals fluids (with R. Hagan). In "New Perspectives in Thermodynamics", Springer-Verlag, 1986, pp. 241-260.
- Uniqueness of non-negative solutions of semilinear equations in (with L.A. Peletier). Journal of Differential Equations, 61 (1986), pp. 380-397.
- A general variational identity (with P. Pucci). Indiana Univ. Mathematics Journal, 35 (1986), pp. 681-703.
- Existence and non-existence theorems for ground states of quasilinear partial differential equations. The anomalous case (with W.-M. Ni). Rome, Acc. Naz. dei Lincei, Atti dei Convegni, vol. 77 (1986), pp. 231-257.
- Non-existence of singular solutions of quasilinear partial differential equations (with W.-M. Ni). Communications on Pure and Applied Mathematics, 39 (1986), pp. 379-399.
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- Asymptotic behavior of ground states of quasilinear elliptic equations with two vanishing parameters (with F. Gazzola). To appear, Joural Inst. Henri Poincare, 2001.
- Cauchy-Liouville and universal boundedness theorems for quasilinear ellptic equations (with H. Zou). To appear, 2002.
- The Harnack inequality for quasilinear elliptic equations in
two dimensions (with P. Pucci). To appear, 2002.

*Updated July 7, 1998*