The Neumann problem for the fractional Laplacian: regularity up to the boundary

Alessandro Audrito, Juan-Carlos Felipe-Navarro, Xavier Ros-Oton

We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if $u$ is a weak solution of $(-\Delta {)}^{s}u=f$ in $\Omega$, $\mathc…