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Research Article | Open Access

The local boundary estimate of weak solutions to fractional p-Laplace equations

Wenjia Li, Guanglan Wang( ), Guoliang Li( )
School of Mathematical Sciences, Linyi University, Linyi 276005, China
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Abstract

In this paper, we investigate weak solutions to equations of fractional p-Laplace type. We obtain several local boundary estimates about weak solutions in Bessel space by the Lipschitz truncation method and the pointwise Hardy inequality. The estimates are global over bounded domains that satisfy an exterior uniform thickness condition, which involves the fractional ( s , p )-capacity.

Keywords

Bessel spacescapacityPoincaré-Sobolev inequalityuniformly (s, p)-thickLipschitz truncation
CLC number: 35R11, 42B25

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 8002-8021
DOI: 10.3934/math.2025367

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Cite this article:
Li W, Wang G, Li G. The local boundary estimate of weak solutions to fractional p-Laplace equations. AIMS Mathematics, 2025, 10(4): 8002-8021. https://doi.org/10.3934/math.2025367

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Received: 22 December 2024
Revised: 25 March 2025
Accepted: 27 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)