Regularity of harmonic functions for anisotropic fractional Laplacian

2007/06/04 by Paweł Sztonyk, Sztonyk, Paweł · 1 citation
Computer Science · Mathematics · #31C05 #47D03 #60G51 #60J35 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.0706.0413

openalex publication_date 2007/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Asymptotic estimates of multi-dimensional stable densities and their applications

Cited by

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

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