53rd Midwest PDE Seminar March 19-21, 2004 Department of Mathematics University of Missouri

Tadeusz Iwaniec Syracuse University
Pucci's conjecture and the Alexandrov Inequality for Elliptic PDEs in the plane

Abstract

The inequality of Alexandrov, Bakel'man and Pucci is a basic tool in the theory of linear elliptic partial differential equations which are not in divergence form. In two dimensions, we will prove the sharp form of maximum principle as conjectured by Pucci in 1966, and give a number of results for the degenerate elliptic PDEs. This is my recent joint work with Kari Astala and Gaven Martin.