Sobolev versus Hölder minimizers for the degenerate fractional p-Laplacian

Iannizzotto A.;MOSCONI, SUNRA JOHANNES NIKOLAJ;SQUASSINA, MARCO

2020-01-01

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Abstract

We consider a nonlinear pseudo-di erential equation driven by the fractional p-Laplacian (−∆)sp 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 Ws,p(Ω) and in the weighted Hölder space Cs0(Ω), respectively, coincide.