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Weighted analytic regularity for the integral fractional Laplacian in polygons
(2021)SAM Research ReportWe 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.Report -
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
(2022)SAM Research ReportWe prove weighted analytic regularity for the solution of the integral frac tional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity result, we prove exponential convergence of the hp FEM on geometric boundary-refined meshes.Report -
Weighted analytic regularity for the integral fractional Laplacian in polyhedra
(2023)SAM Research ReportOn 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 ...Report