See the syllabus on my web page.

Reading assignment: March 26th 2013

Read section 8.1-8.3 in Evans, and Lax-Milgram theorem. Write a summary of what you think is the most important.

Classes and Reading:

- Week 1 : 5.2
- Week 2 : 5.3, 5.4, 5.5, 5.6, 5.7

Midterm: March 28th 2013. See the subject and a correction.

Homework assignments:

- Thursday Feb. 14th: Chapter 5, section 5.5, exercises 3, 5, 8, 14, 15.
- Tuesday March 12th: List of exercises. Please give the homework directly to the grader, Sam Punshon-Smith. Here is a solution.

Projects assignments: The 1st project is due Thursday March 28th 2013.

Suggested readings for the 1st project:

- F. Bethuel, H. Brezis, F. Helein, Asymptotics for the minimization of a Ginzburg-Landau functional,
Calculus of Variations and Partial Differential Equations, May 1993, Volume 1, Issue 2, pp 123-148.
- L. Caffarelli's lecture notes on second order elliptic equations (link here).

- G. Crippa, C. DeLellis, Estimates and regularity results for the DiPerna-Lions flow (available on C. DeLellis webpage)
- G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. MATH. ANAL. Vol. 20, No. 3, pp. 608-623, May 1989.
- P.L. Lions, B. Perthame, E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related questions. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 7. Number I. January 1994.
- Yudovich well posedness for 2d Euler, see for instance J.Y. Chemin, Perfect Incompressible Fluids, pages 85-93.