Weighted analytic regularity for the integral fractional Laplacian in polygons

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.

References in corpus (3)

• Numerical methods for nonlocal and fractional models
• Local convergence of the FEM for the integral fractional Laplacian
• Gevrey regularity for integro-differential operators

Cited by in corpus (4)

• Fractional Dissipative PDEs
• Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons
• Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
• An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM