Regularity theory for classes of local and non-local degenerate elliptic equation

Abstract

The goal of this project is to study Partial Differential Equations (PDEs). In particular, we are interested in regularity theory for degenerate equations and free boundaries related to transmission problems. The present project consists in the study of some important classes of problems: first, we study fully nonlinear degenerate equations, whose aim is to prove global regularity in Sobolev spaces. In the sequel, we would like to prove properties for level sets and critical sets of solutions to an equation related to the p-Laplacian operator. Finally, we study transmission problems involving non-local operators whose aim is to prove existence and regularity for the solutions and properties of the free boundary. (AU)