A survey on boundary regularity for the fractional p-Laplacian and its applications

Abstract

We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary Hölder continuity of the solutions of related Dirichlet problems. Then, we present some applications of such results to general nonlinear elliptic equations of fractional order, treated via either variational or topological methods.