Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2022). Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons. SIAM Journal on Mathematical Analysis, 54(6), 6323–6357. https://doi.org/10.1137/21M146569X
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.
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Project title:
Numerische Methoden Höherer Ordnung für nichtlokale Operatoren: F 6507-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
