Weighted analytic regularity for the integral fractional Laplacian in polygons
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2021-12
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Report
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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.
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published
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2021-41
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Seminar for Applied Mathematics, ETH Zurich
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Subject
fractional Laplacian; analytic regularity; corner domains; eighted Sobolev spaces
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03435 - Schwab, Christoph / Schwab, Christoph
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