|Introduction to PDE|
|Time：||Tue/Thu 10:10-12:00, 2015-03-05~ 2015-04-28|
|Instructor：||Leon Simon [Stanford University]|
|Place：||Conference Room 4, Floor 2, Jin Chun Yuan West Building|
This course will provide an introduction to Partial Differential Equations at a beginning/intermediate graduate level and is recommended for those planning to specialize in geometry and/or analysis.
Topics will include some of the basic theory of both linear and non-linear elliptic equations, including: Weak solutions in Sobolev space and regularity theory for linear elliptic problems, Spectrum of self-adjoint operators, heat kernel and Weyl's asymptotic formula, Schauder theory for elliptic and parabolic problems, non-linear problems with small data, maximum principles and the method of sub and super solutions for semi-linear and quasilinear problems, Leray Schauder theory, Quasilinear problems including the mean curvature equation, Lyapunov-Schmidt and applications, Unique continuation and the frequency function.
The course will assume a good background in Mathematical Analysis at beginning graduate level. No particular background in PDE will be assumed.
On-line lecture notes will be provided during the course of the lectures.