Year: 2022
Author: Yanan Shan, Hongya Gao
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 320–330
Abstract
Denote $$ {\cal K} _{\psi, \theta} (\Omega) =\left\{ v\in W^{1,p} (\Omega) : v\ge \psi, \mbox { a.e. and } v-\theta \in W_0^{1,p} (\Omega) \right\}, $$ where $\psi$ is any function in $\Omega \subset \mathbb R^N$, $N\ge 2$, with values in $\mathbb R \cup \{\pm \infty\}$ and $\theta $ is a measurable function. This paper deals with global integrability for $u \in {\cal K}_{\psi, \theta}$ such that
$$ \int_\Omega \langle {\cal A} (x,\nabla u), \nabla (w-u) \rangle {\rm d}x \ge \int_\Omega \langle F, \nabla (w-u) \rangle {\rm d}x, \ \ \forall\ w \in {\cal K}_{\psi,\theta} (\Omega), $$ with $|{\cal A} (x,\xi)| \approx |\xi| ^{p-1}$, $1<p<N$. Some global integrability results are obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n4.2
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 320–330
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Global integrability obstacle problem A-harmonic equation.
Author Details
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