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 GiorgiNashMoser theory 
Notes 

8 
Feb 5 
Holder continuity: The de GiorgiNashMoser theory 
Notes 
HW 2 due 
9 
Feb 8 
Holder continuity: The de GiorgiNashMoser theory 
Notes 

10 
Feb 10 
Holder continuity: The de GiorgiNashMoser theory 
Notes 

11 
Feb 12 
Holder continuity: The de GiorgiNashMoser 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 HamiltonJacobi Bellman equation 
Notes 

27 
Mar 30 
The HamiltonJacobi 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 
