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Weighted analytic regularity for the integral fractional Laplacian in polygons

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

(Report number 2021-41)

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.

Keywords: fractional Laplacian, analytic regularity, corner domains, weighted Sobolev spaces

@Techreport{FMMS21_983,
  author = {M. Faustmann and C. Marcati and J.M. Melenk and Ch. Schwab},
  title = {Weighted analytic regularity for the integral fractional Laplacian in  polygons},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-41},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-41.pdf },
  year = {2021}
}

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