Fine boundary regularity for the degenerate fractional p-Laplacian

Antonio Iannizzotto;Sunra Mosconi;Marco Squassina

2020-01-01

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Abstract

We consider a nonlocal equation driven by the fractional p-Laplacian with s ∈ ]0, 1[ and p>2 (degenerate case), with a bounded reaction f and Dirichlet type conditions in a smooth domain Ω. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution u of such equation exhibits a weighted Hölder regularity up to the boundary, that is, u/d^s ∈ C^α(Ω) for some α ∈ ]0, 1[, d being the distance from the boundary.