MATH 6200 - Partial Differential Equations

Laurent Saloff-Coste, spring 2016.

The basic modern 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 weak solutions. We also study parabolic and hyperbolic problems. Time permitting, we will look at some nonlinear problems as well.

(This course is totally independent of MATH 6190, although we use the same book — Lawrence C. Evans, Partial Differential Equations. Most of the material corresponds to Chapters 5-7 plus selected topics from 8,10, and 11.)