Regularity of harmonic functions for anisotropic fractional Laplacians
Paweł Sztonyk · Mathematische Nachrichten · 2010
Abstract We prove that bounded harmonic functions of anisotropic fractional Laplacians are Hölder continuous under mild regularity assumptions on the corresponding Lévy measure. Under some stronger assumptions the Green function, Poisson kernel and the harmonic functions are even differentiable of order up to three (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)