Weighted analytic regularity for the integral fractional Laplacian in polyhedra
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2023-07
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Report
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Abstract
On polytopal domains in 3D, we prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian with analytic right-hand side. Employing the Caffarelli-Silvestre extension allows 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 control of higher order derivatives.
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published
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2023-31
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Fractional Laplacian; Analytic regularity; Corner domains; Weighted Sobolev spaces
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03435 - Schwab, Christoph / Schwab, Christoph
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