Weighted analytic regularity for the integral fractional Laplacian in polygons

12/15/2021

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by   Markus Faustmann, et al.

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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.