Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab · SIAM Journal on Mathematical Analysis · 2022
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 vertex-edge neighborhoods.