Math 282: Elliptic PDE
Instructor: M. Stern

This course develops the tools needed in the study 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.  We will study asymptotic
behavior of eigenfunctions of Schrodinger operators.  Further topics may be
chosen from mildly nonlinear elliptic problems if time permits.