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

2005/07/27 by Krzysztof Bogdan, Bogdan, Krzysztof, Paweł Sztonyk +1 · 1 citation
Mathematics · #31C05 #47D03 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:31C05 #msc:47D03

paper · pdf · doi:10.48550/arxiv.math/0507579

28 pages

arxiv created 2005/07/27 · arxiv updated 2009/12/01

Abstract

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.

Cited by

• Isolated Singularities and Measure Data Problems for Semilinear Equations Driven by Stable Lévy Operators

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