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 1,1 domain 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 C s ( ) for any p > 1 and, in the singular case p ∈ (1, 2), that u/d s has a Hölder continuous extension to the closure of , d (x) meaning the distance of x from the complement of .This last result is the singular counterpart of the one in 30, where the degenerate case p 2 is considered.