MATH 6200: Partial Differential Equations (Spring 2010)
Instructor: Lars Wahlbin
This course is totally independent of MATH 6190, although we use the same book, Lawrence C. Evans, Partial Differential Equations. The basic theory of second-order elliptic boundary-value problems is studied in a setting of function spaces called Sobolev spaces. So, we start by studying those spaces. In a Hilbert space setting, we then study the questions of existence, uniqueness and regularity of solutions. We also study parabolic and hyperbolic time-dependent problems. The material corresponds to Chapters 5, 6, and 7 in Evans' book. If time permits, we may look at some nonlinear problems.