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arXiv · 2307.11679

Weighted analytic regularity for the integral fractional Laplacian in polyhedra

Markus Faustmann·Carlo Marcati·Jens Markus Melenk·Christoph Schwab
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Abstract

On polytopal domains in $\mathbb{R}^3$, 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 weighted, analytic control of higher order solution derivatives.

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Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab. 2023-07-21. Weighted analytic regularity for the integral fractional Laplacian in polyhedra. https://arxiv.org/abs/2307.11679

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