Sobolev versus Hölder minimizers for the degenerate fractional [formula omitted]-Laplacian

Abstract

We consider a nonlinear pseudo-differential equation driven by the fractional p-Laplacian (−Δ)ps with s∈(0,1) and p⩾2 (degenerate case), under Dirichlet type conditions in a smooth domain Ω. We prove that local minimizers of the associated energy functional in the fractional Sobolev space W0s,p(Ω) and in the weighted Hölder space Cs0(Ω¯), respectively, coincide.