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.
Sobolev versus Hölder minimizers for the degenerate fractional p-Laplacian
Iannizzotto A.;MOSCONI, SUNRA JOHANNES NIKOLAJ;SQUASSINA, MARCO
2020-01-01
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.
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