Regularity of harmonic functions for anisotropic fractional Laplacian

Details Regularity of harmonic functions for anisotropic fractional Laplacian Regularity of harmonic functions for anisotropic fractional Laplacian

2007-06-04

arxiv.org/abs/0706.0413v1

Mathematics

Probability

36 pages

Scientific paper

We prove that bounded harmonic functions of anisotropic fractional Laplacians
are H\"older continuous under mild regularity assumptions on the corresponding
L\'evy measure. Under some stronger assumptions the Green function, Poisson
kernel and the harmonic functions are even differentiable of order up to three.

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