Weighted analytic regularity for the integral fractional Laplacian in polyhedra

Abstract

On polytopal domains in ℝ3, we prove weighted analytic regularity of solutions to the Dirichlet problem for the shifted integral fractional Laplacian with analytic right-hand side. Employing the Caffarelli-Silvestre extension allows one to localize the problem and to decompose the regularity estimates into results on vertex, edge, face, vertex-edge, vertex-face, edge-face and vertex-edge-face neighborhoods of the boundary. Using tangential differentiability of the extended solutions, a bootstrapping argument based on Caccioppoli inequalities on dyadic decompositions of the neighborhoods provides weighted, analytic control of higher-order solution derivatives.