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Weighted analytic regularity for the integral fractional Laplacian in polyhedra

by M. Faustmann and C. Marcati and J. Melenk and Ch. Schwab

(Report number 2023-31)

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.

Keywords:

@Techreport{FMMS23_1068,
  author = {M. Faustmann and C. Marcati and J. Melenk and Ch. Schwab},
  title = {Weighted analytic regularity for the integral fractional Laplacian in polyhedra },
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-31},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-31.pdf },
  year = {2023}
}

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