Fall 2022 M541 Partial Differential Equations II

Description

Sobolev spaces; weak solutions to elliptic PDE; elliptic regularity theory; spectral theory of elliptic operators; linear parabolic and hyperbolic equations.

Homework

HW will be assigned on Thursday of each week, and will be due on the following Thursday. The homework problems form an integral part of the course; they are easily the most reliable check of your progress in assimilating the material in a manner which is sufficiently deep to allow you to solve problems that are at least one level removed from routine application of definitions and formulas. It is encouraged that you discuss the problems in general terms with your peers, but it expected that what you hand in is your own work, and not a joint project of several people.

Exams

There will be two (in-class) exams: a mid-term and a final.

Grading

The final grade will be based on HW: 40, Midterm: 30,  Final: 30

Text and References

• PDEs, Evans, AMS (required) 
• D. Gilbarg  and N. S. Trudinger, Elliptic partial differential equations of second order, Springer
• Jacques-Louis Lions, Quelques Methodes de Resolution des Problemes aux Limits non Lineares, Dunod, 1969.