[Plenary Lecture] Nonlinear Potentials in PDE: from uniformly to nonuniformly elliptic problems

Speaker: Giuseppe Mingione, University of Parma, Italy

Title: Nonlinear Potentials in PDE: from uniformly to nonuniformly elliptic problems

Abstract: In these two talks I will summarize a series of recent results in regularity theory of elliptic PDEs, where nonlinear potentials play a key role in order to get sharp a priori regularity estimates. In particular, in the second talk I will concentrate on nonuniformly elliptic problems, showing a few new techniques eventually leading to the proof of Schauder estimates. These involve a delicate use of a general class of nonlinear potentials.