Welcome to the MATH 836 website for this semester
This is what the guide says we will do...
Sobolev spaces, potential theory, variational methods for elliptic equations, inverse problems. PREREQ: MATH806.
This is where and when...
MWF
10:10AM  11:00AM at Drake Hall 074
The book
Sandro Salsa. Partial Differential Equations in Action. From Modelling to Theory. Chapters 3, 6, 7 and 8.
Newsbox
(05/06) Final problemsheet.
We will work on these problems in the final
lectures. 
Table with the detailed schedule
Click on the Problems cells to see or download the problem collections. Sections in the book are given as help to read a possibly different point of view. Students are supposed to be able to solve all the recommended problems.
Week 
Lecture 
Section 
Description 
Problems 

1 
02/04 
M 
7.17.2 
I. DISTRIBUTIONS 1. Test functions 
Problem sheet #1 
02/06 
W 
7.3 
2. Distributions 

02/08 
F 
7.4 
3. Convergence and
differentiation 

2 
02/11 
M 
7.4 
4. Vanishing gradients and fundamental
solutions 

02/13 
W 
7.7.2 
II. THE
HOMOGENEOUS DIRICHLET PROBLEM 1. The Sobolev space H^1 

02/15 
F 
7.2 
2. Cutoff, mollification and density 
Problem sheet
#2 

3 
02/18 
M 
7.7.3 
3. H^1_0 and the
PoincareFriedrichs inequality 

02/20 
W 
4. Three forms of the
Dirichlet problem 

02/22 
F 
6.5 
5. The RieszFrechet
representation as an existence theorem 
EXAM
#1 DUE 

4 
02/25 
M 
III.
NONHOMOGENEOUS DIRICHLET B.C. 1. Lipschitz transformations and Lipschitz domains 

02/27 
W 
7.8 
2. Localization and pullback 

03/01 
F 
7.8 
3. The extension theorem  
5 
03/04 
M 
7.9 
4. The trace theorem  Problem sheet #3 
03/06 
W 
5. The kernel and image of the trace operator  
03/08 
F 
8.4.1 
6. The nonhomogeneous Dirichlet problem  
6 
03/11 
M 
IN CLASS TEST 
EXAM #2 

03/13 
W 
6.6 
IV.
NONSYMMETRIC AND COMPLEX PROBLEMS 1. The LaxMilgram lemma 

03/15 
F 
8.5.2 
2. Convectiondiffusion problems 

7 
03/18 
M 
3. Complex spaces and
complexified spaces 
Problem sheet #4 

03/20 
W 
4. Resolvent equations 

03/22 
F 
INTERMISSION. Linear elasticity 

8 
Spring break 

9 
04/01 
M 
V. THE NEUMANN PROBLEM 1. H(div) and the normal trace 

04/03 
W 
2. Easy problems with
Neumann conditions 

04/05 
F 
3. The DenyLions theorem
and a flavor of compactness 

10 
04/08 
M 
4. Neumann problems for elliptic equations 
EXAM #3 DUE  
04/10 
W 
5. The Neumann problem for the Poisson equation  
04/12 
F 
VI. THE
FREDHOLM ALTERNATIVE AND HELMHOLTZ EQUATIONS 1. The RellichKondrachov theorem 

11 
04/15 
M 
2. The Fredholm alternative in the
selfadjoint case 
Problem sheet #5 

04/17 
W 
3. Helmholtz equation and
Neumann revisited 

04/19 
F 
4. Impedance conditions
and the bilaplacian 

12 
04/22 
M 
5. General Fredholm theorems  Problem sheet
#6 

04.24 
W 
6. Convectiondiffusion problems 

04/26 
F 
VII.
EIGENVALUES OF ELLIPTIC OPERATORS 1. Eigenvalues of elliptic operators 

13 
04/29 
M 
IN CLASS TEST (five
problems, closed book) 
EXAM #4 

05/01 
W 
2. The HilbertSchmidt
theorem 

05/03 
F 
3. Proofs and applications 

14 
05/06 
M 
4. Series characterizations of Sobolev
spaces 

05/08 
W 
5. More eigenvalue problems 
Problem sheet #7  
05/10 
F 

15 
05/13 
M 

05/17 
F 
EXAM
#5 due 

And
we are done 