Weighted analytic regularity for the integral fractional Laplacian in polygons

Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab

Abstract: We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem through the Caffarelli-Silvestre extension and study the tangential differentiability of the extended solutions, followed by bootstrapping based on Caccioppoli inequalities on dyadic decompositions of vertex, edge, and edge-vertex neighborhoods.