A quantitative second order Sobolev regularity for (inhmogeneous) normalized $p(\cdot)$-Laplace equations

Yuqing Wang; Yuan Zhou

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arXiv · 2403.03784

A quantitative second order Sobolev regularity for (inhmogeneous) normalized $p(\cdot)$-Laplace equations

Yuqing Wang·Yuan Zhou

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Abstract

Let $Ω$ be a domain of $\mathbb R^n$ with $n\ge 2$ and $p(\cdot)$ be a local Lipschitz funcion in $Ω$ with $1 1$ and $\sup_Up(x)<3+\frac2{n-2}$, one has $D^2u\in L^{2+δ}(U)$ locally with a quantitative upper bound, and also with a pointwise upper bound $$|D^2u|^2\le -C\sum_{1\leq i 0$ and $C\geq 1$ are independent of $u$. These extend the related results obtaind by Adamowicz-Hästö \cite{AH2010} when $n=2$ and $β=0$.

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Yuqing Wang, Yuan Zhou. 2024-03-06. A quantitative second order Sobolev regularity for (inhmogeneous) normalized $p(\cdot)$-Laplace equations. https://arxiv.org/abs/2403.03784

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