Sobolev versus Hölder minimizers for the degenerate fractional p-Laplacian

Abstract We consider a nonlinear pseudo-differential equation driven by the fractional p -Laplacian ( − Δ ) p s 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 W 0 s , p ( Ω ) and in the weighted Holder space C s 0 ( Ω ¯ ) , respectively, coincide.