820 - Partial Differential Equations

Study of Holder and L^p estimates for elliptic operators, beginning
with theory of harmonic functions. Extension of the theory to
non-compact spaces using weighted Holder and Sobolev spaces, indicial
roots, and Fredholm properties. Separation of variables for
rotationally symmetric operators. Index theory on manifolds which are
asymptotically flat or asymptotically cylindrical.