The fractional Malmheden theorem

DOI10.3934/mine.2023024arXiv2203.06923OpenAlexW4226141732MaRDI QIDQ6195564

Giovanni Giacomin, Enrico Valdinoci, Serena Dipierro

Publication date: 14 March 2024

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.06923

zbMATH Keywords

Harnack inequalityPoisson kernelfractional LaplacianSchwarz theoremgeometric properties of harmonic functionsMalmheden theorem

Mathematics Subject Classification ID

Real functions (26-XX) Potential theory (31-XX)

Cites Work

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• Nonlocal diffusion and applications
• All functions are locally \(s\)-harmonic up to a small error
• A new formulation of Harnack's inequality for nonlocal operators
• Malmheden's theorem revisited
• Some observations on the Green function for the ball in the fractional Laplace framework
• Functional analysis, Sobolev spaces and partial differential equations
• Description of an ecological niche for a mixed local/nonlocal dispersal: an evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes
• On the mean value property of fractional harmonic functions
• A note on Poisson’s integral
• The Geometry of Harmonic Functions
• An Extension Problem Related to the Fractional Laplacian

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