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Regularity of harmonic functions for anisotropic fractional Laplacians

✍ Scribed by Paweł Sztonyk

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
230 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

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)

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