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

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 satisf...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 4; pp. 8002 - 8021
Main Authors Li, Wenjia, Wang, Guanglan, Li, Guoliang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2025
Subjects
bessel spaces
capacity
lipschitz truncation
poincaré-sobolev inequality
uniformly $ (s, p) $-thick
Online AccessGet full text
ISSN2473-6988
2473-6988
DOI10.3934/math.2025367

Cover

More Information
Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025367