Fine boundary regularity for the singular fractional p-Laplacian

Iannizzotto A.;Mosconi S.

2024-01-01

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Abstract

We study the boundary weighted regularity of weak solutions u to a s-fractional p-Laplacian equation in a bounded C1,1 domain Ω with bounded reaction and nonlocal Dirichlet type boundary condition, with s∈(0,1). We prove optimal up-to-the-boundary regularity of u, which is Cs(Ω‾) for any p>1 and, in the singular case p∈(1,2), that u/dΩs has a Hölder continuous extension to the closure of Ω, dΩ(x) meaning the distance of x from the complement of Ω. This last result is the singular counterpart of the one in [30], where the degenerate case p⩾2 is considered.