Instructor: Igor Verbitsky

Description: We will start with basic properties of subharmonic functions, classical potential operators, and integral inequalities of Sobolev type. Some nonlinear versions, including Wolff's potentials associated with the p-Laplacian and k-Hessian operators are to be treated as well. Global and local estimates of solutions to quasilinear and fully nonlinear elliptic PDE obtained very recently by Serrin and Zou, Trudinger and Wang, and Labutin will be discussed. The usual lecture format will be complemented by presentations given by the participants.

Prerequisite: Basic knowledge of Real and Complex Analysis.