Fine boundary regularity for the singular fractional p-Laplacian

We study the boundary weighted regularity of weak solutions u to a s-fractional p-Laplacian equation in a bounded C-1,C-1 domain Omega with bounded reaction and nonlocal Dirichlet type boundary condition, with s is an element of (0, 1). We prove optimal up-to-the-boundary regularity of u, which is C-s (sic Omega) for any p > 1 and, in the singular case p is an element of (1, 2), that u/d(Omega)(s) has a Holder continuous extension to the closure of Omega, d(Omega)(x) meaning the distance of x from the complement of Omega. This last result is the singular counterpart of the one in [30], where the degenerate case p >= 2 is considered. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).