Schedule


Lecture Date Topic Reading Notes
Jan 20 No class
2 Jan 22 Difference quotients Evans 5.8
3 Jan 25 Difference quotients Evans 5.8
4 Jan 27 Interior regularity Evans 6.3
5 Jan 29 Higher interior regularity Evans 6.3 HW 1 due
6 Feb 1 Global regularity up to boundary Evans 6.3
7 Feb 3 Holder continuity: The de Giorgi-Nash-Moser theory Notes
8 Feb 5 Holder continuity: The de Giorgi-Nash-Moser theory Notes HW 2 due
9 Feb 8 Holder continuity: The de Giorgi-Nash-Moser theory Notes
10 Feb 10 Holder continuity: The de Giorgi-Nash-Moser theory Notes
11 Feb 12 Holder continuity: The de Giorgi-Nash-Moser theory Notes HW 3 due
Feb 15 Holiday (no class)
12 Feb 17 Weak/Strong maximum principles Evans 6.4
13 Feb 19 Eigenvalues and eigenvectors Evans 6.5 HW 4 due
14 Feb 22 Negative Sobolev spaces Evans 5.9
15 Feb 24 Parabolic equations: Existence Evans 7.1
16 Feb 26 Parabolic equations: Uniqueness Evans 7.1 HW 5 due
17 Feb 29 Calculus of Variations Evans 8.1
18 Mar 2 Calculus of Variations Evans 8.2
19 Mar 4 Calculus of Variations Evans 8.2 HW 6 due
20 Mar 7 Calculus of Variations Evans 8.4 MT Start
21 Mar 9 Fixed point methods Evans 9.2
22 Mar 11 Fixed point methods Evans 9.2 MT Due
23 Mar 14 Intro to viscosity solutions Notes
24 Mar 16 Definitions and consistency Notes
25 Mar 18 Comparison principle Notes HW 7 due
Mar 21 No class
Mar 23 No class
Mar 25 No class
26 Mar 28 The Hamilton-Jacobi Bellman equation Notes
27 Mar 30 The Hamilton-Jacobi Bellman equation Notes
28 Apr 1 Method of vanishing viscosity Notes
29 Apr 4 Rate of convergence Notes
30 Apr 6 Semiconcavity and better rates Notes
31 Apr 8 Boundary conditions in the viscosity sense Notes HW 8/9 due
32 Apr 11 Comparison on unbounded domains Notes
33 Apr 13 The Perron method Notes
34 Apr 15 Monotone finite difference schemes Notes HW 10 due
35 Apr 18 Fast Marching and Fast Sweeping Notes
36 Apr 20 Monotone schemes are 1st order Notes
37 Apr 22 Convergence rate Notes HW 11 due
38 Apr 25 Homogenization theory Notes
39 Apr 27 Homogenization theory Notes
40 Apr 29 TBD Notes HW 12 due
41 May 2 TBD Notes