Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian

Details Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian

2005-07-27

arxiv.org/abs/math/0507579v1

Mathematics

Probability

28 pages

Scientific paper

We characterize those homogeneous translation invariant symmetric non-local
operators with positive maximum principle whose harmonic functions satisfy
Harnack's inequality. We also estimate the corresponding semigroup and the
potential kernel.

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