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arXiv · 2112.08151

Weighted analytic regularity for the integral fractional Laplacian in polygons

Markus Faustmann·Carlo Marcati·Jens Markus Melenk·Christoph Schwab
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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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Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab. 2021-12-15. Weighted analytic regularity for the integral fractional Laplacian in polygons. https://doi.org/10.1137/21m146569x

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