MATH 6200 - Partial Differential Equations

Alex Vladimirsky, spring 2014.

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 time-dependent 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.)