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Weighted analytic regularity for the integral fractional Laplacian in polygons (2112.08151v2)
Published 15 Dec 2021 in math.AP, cs.NA, and math.NA
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.