Complete schedule for MATH/AMSC 674, Spring 2013 (subject to changes during the course)
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.
- 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.
- Yudovich well posedness for 2d Euler, see for instance J.Y. Chemin, Perfect Incompressible Fluids, pages 85-93.