AM 224 SYLLABUS, Spring 2006
AM 223-224 (MA 237-238) is the core graduate sequence on partial differential
equations. In the first semester, the focus was
on the basic theory of linear equations. This semester, we will
mainly study nonlinear equations. The plan is
to cover as much is possible of the following topics:
- Scalar conservation laws and Hamilton-Jacobi equations.
- Sobolev inequalities and Sobolev spaces.
- The direct method in the calculus of variations.
- Elliptic regularity.
- Symmetric hyperbolic systems.
Prerequisites: Real analysis (AM 211, MA 221 or equivalent) and AM 223
Textbooks: The two main sources for the class this semester will be
As in AM 223, a few representative examples will be treated in depth,
and this will often mean consulting other sources, including original
papers. To the extent possible, I will try to hand out notes.
The following sources will be useful at different points:
- L. C. Evans, Partial differential equations , AMS 1998.
- L. C. Evans, Weak convergence methods for nonlinear
PDE , AMS, 1988.
- C.M. Dafermos, Hyperbolic conservation laws in
continuum physics , Springer, 200.
- F. John, Partial differential equations , Springer 1981.
- D. Gilbarg and N. Trudinger, Elliptic partial differential
equations of second order , Springer 2001.
- M. Struwe, Variational methods ,
Here is a transcript of the lectures by
Here is Andreas' English translation of Hopf's
paper on the Navier-Stokes equations.
HW 1 , Solutions .
HW 2 , Solutions .
HW 3 , Solutions .
HW 4 , Solutions .
HW 5 , Solutions .
HW 6 , Solutions .
File translated from
On 24 Jan 2006, 16:47.