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

Wenjia Li; Guanglan Wang; Guoliang Li; Wenjia Li; Guanglan Wang; Guoliang Li

doi:10.3934/math.2025367

AIMS Mathematics

2025, Volume 10, Issue 4: 8002-8021. doi: 10.3934/math.2025367

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

School of Mathematical Sciences, Linyi University, Linyi 276005, China

Received: 22 December 2024 Revised: 25 March 2025 Accepted: 27 March 2025 Published: 07 April 2025
MSC : 35R11, 42B25

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.
- Bessel spaces,
- capacity,
- Poincaré-Sobolev inequality,
- uniformly $ (s, p) $-thick,
- Lipschitz truncation
Citation: Wenjia Li, Guanglan Wang, Guoliang Li. The local boundary estimate of weak solutions to fractional $ p $-Laplace equations[J]. AIMS Mathematics, 2025, 10(4): 8002-8021. doi: 10.3934/math.2025367

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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.

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