The Poisson’s problem for the Laplacian with Robin boundary condition in non-smooth domains
The Poisson’s problem for the Laplacian with Robin boundary condition in non-smooth domains
Given a bounded Lipschitz domain \Omega\subset {\mathbb R}^n , n\geq 3 , we prove that the Poisson's problem for the Laplacian with right-hand side in L^p_{-t}(\Omega) , Robin-type boundary datum in the Besov space B^{1-1/p-t,p}_{p}(\partial \Omega) and non-negative, non-everywhere vanishing Robin coefficient b\in L^{n-1}(\partial \Omega) , is uniquely solvable in …