Math 282: Elliptic Partial Differential Equations


This course develops the tools needed in rigorous analysis of elliptic
P.D.E.'s . We will begin with a review of the Fourier transform and
distributions. We review aspects of harmonic functions and study the
representation of solutions of Laplacian u = f by singular integrals. We
will study Sobolev spaces of functions having a fxied number of derivatives
in a weak sense in L^2. We will then study existence and regularity of
elliptic boundary value problems from this L^2 point of view. We will
frequently show how to derive related results from a variational approach.
Further topics may be chosen from mildly nonlinear elliptic problems if time
permits. Prerequisites: Math 232 (PDE I), Math 241 (real analysis), or
having equivalent background. Text book: Folland, Introduction to Partial
Differential Equations, second edition. Reference book: Evans' P.D.E.