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arXiv · 2606.26610

Self-improving properties for the fractional $p$-Laplacian via nonlinear commutators

Ho-Sik Lee·Kyeong Song
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Abstract

We investigate a class of nonlocal equations whose leading operator is modeled on either the fractional $p$-Laplacian or the regional fractional $p$-Laplacian, $p \in (1,\infty)$. We prove local self-improving properties of weak solutions to the fractional $p$-Laplacian in the case $p\in(1,\infty)$ with non-integrable right-hand side, as well as to the regional fractional $p$-Laplacian in the subquadratic case $1 < p < 2$, by extending the nonlinear commutator estimates developed by Schikorra (Math. Ann. 366 (1-2):695--720, 2016).

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Ho-Sik Lee, Kyeong Song. 2026-06-25. Self-improving properties for the fractional $p$-Laplacian via nonlinear commutators. https://arxiv.org/abs/2606.26610

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