Schedule


The class schedule below will be updated on a weekly basis. The class will mainly follow the lecture notes below, which will be periodically updated.

Calder, Jeff. Lecture notes on viscosity solutions. [pdf]. (Updated Nov 2018)

Lecture Date Topic Notes
1 Sep 5 Motivational examples Slides
2 Sep 7 Motivational examples
3 Sep 10 Motivation and definitions Slides
4 Sep 12 Motivation and definitions
5 Sep 14 Comparison principle Slides
6 Sep 17 Comparison principle
7 Sep 19 Hamilton-Jacobi-Bellman Equation Slides
8 Sep 21 Hamilton-Jacobi-Bellman Equation HW 1 due
9 Sep 24 Method of vanishing viscosity Slides
10 Sep 26 Method of vanishing viscosity
11 Sep 28 Semiconcavity
12 Oct 1 Boundary conditions in viscosity sense Slides
13 Oct 3 Boundary conditions in viscosity sense
14 Oct 5 The Perron method HW 2 due
15 Oct 8 The Perron method Slides
16 Oct 10 Inf/Sup Convolutions Slides
17 Oct 12 Inf/Sup Convolutions
18 Oct 15 Finite difference schemes Slides
19 Oct 17 Finite difference schemes
20 Oct 19 Finite difference schemes HW 3 due
21 Oct 22 Finite difference schemes
22 Oct 24 Finite difference schemes
23 Oct 26 Homogenization Slides
24 Oct 29 Homogenization
25 Oct 31 Discontinuous coefficients Slides
26 Nov 2 Discontinuous coefficients HW 4 due
27 Nov 5 Second order equations Slides
28 Nov 7 Second order equations
29 Nov 9 Second order equations
30 Nov 12 Second order equations
Nov 14 No class
31 Nov 16 Second order equations HW 5 due
32 Nov 19 Second order equations
33 Nov 21 Second order equations
Nov 23 Thanksgiving
34 Nov 26 Carter Chain: Pegden, Wesley, and Charles K. Smart. "Convergence of the Abelian sandpile." Duke Mathematical Journal 162.4 (2013): 627-642.
35 Nov 28 Drisana Mosaphir: Zhao, Hongkai. "A fast sweeping method for eikonal equations." Mathematics of computation 74.250 (2005): 603-627.
36 Nov 30 Shiqiang Xia: Oberman, Adam M. "A convergent monotone difference scheme for motion of level sets by mean curvature." Numerische Mathematik 99.2 (2004): 365-379.
37 Dec 3 Zanbing Dai: Manfredi, Juan, Mikko Parviainen, and Julio Rossi. "An asymptotic mean value characterization for p-harmonic functions." Proceedings of the American Mathematical Society 138.3 (2010): 881-889.
38 Dec 5 Brendan Cook: Levine, Lionel, Wesley Pegden, and Charles K. Smart. "Apollonian structure in the Abelian sandpile." Geometric and functional analysis 26.1 (2016): 306-336.
39 Dec 7 Amber Yuan: Ishii, Hitoshi, and Paola Loreti. "Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems." SIAM Journal on Mathematical Analysis 37.2 (2005): 411-437.
40 Dec 10 Wenjie Lu: Evans, Lawrence C., H. Mete Soner, and Panagiotis E. Souganidis. "Phase transitions and generalized motion by mean curvature." Communications on Pure and Applied Mathematics 45.9 (1992): 1097-1123.
41 Dec 12 Montie Avery: Evans, Lawrence C., H. Mete Soner, and Panagiotis E. Souganidis. "Phase transitions and generalized motion by mean curvature." Communications on Pure and Applied Mathematics 45.9 (1992): 1097-1123.