The Poisson equation from non-local to local

Umberto Biccari, Víctor Hernández-Santamaría

We analyze the limit behavior as $s\to 1^{-}$ of the solution to the fractional Poisson equation $(-\Delta {)}^s{u}_s=f_s$, $x\in \Omega$ with homogeneous Dirichlet boundary conditions $u_s\equiv 0…