Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case

Fuente: arXiv
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Main Authors: Li, Dingding, Zhang, Chao
Format: Preprint
Published: 2025
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author Li, Dingding
Zhang, Chao
author_facet Li, Dingding
Zhang, Chao
contents We investigate the interior Sobolev regularity of weak solutions to the nonlocal $(1, p)$-Laplace equations in the superquadratic case $p\ge 2$. As a product, the explicit Hölder continuity estimates of weak solutions are derived. The proof relies on a detailed analysis of the structural characteristics of $(1, p)$-growth in the nonlocal setting, combined with the finite difference quotient method, tail estimates, refined energy estimates, and a Moser-type iteration scheme.
format Preprint
id arxiv_https___arxiv_org_abs_2505_23288
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case
Li, Dingding
Zhang, Chao
Analysis of PDEs
We investigate the interior Sobolev regularity of weak solutions to the nonlocal $(1, p)$-Laplace equations in the superquadratic case $p\ge 2$. As a product, the explicit Hölder continuity estimates of weak solutions are derived. The proof relies on a detailed analysis of the structural characteristics of $(1, p)$-growth in the nonlocal setting, combined with the finite difference quotient method, tail estimates, refined energy estimates, and a Moser-type iteration scheme.
title Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case
topic Analysis of PDEs
url https://arxiv.org/abs/2505.23288