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 smooth domain $\mathrm{\Omega }$ with bounded reaction and nonlocal Dirichlet type boundary condition, in the singular case $p\in (1,2)$ and with $s\in (0,1)$. We prove that $u\mathrm{/}{\mathrm{d}}_{\mathrm{\Omega }}^s$ has a $\alpha$-Hölder continuous extension to the closure of $\mathrm{\Omega }$, ${\mathrm{d}}_{\mathrm{\Omega }}(x)$ meaning the distance of $x$ from the complement of $\mathrm{\Omega }$. This result corresponds to that of ref. [28] for the degenerate case $p\ge 2$.