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2019 The long-time behavior of weighted $p$-Laplacian equations
Shan Ma, Hongtao Li
Topol. Methods Nonlinear Anal. 54(2A): 685-700 (2019). DOI: 10.12775/TMNA.2019.064

Abstract

In this work we study weighted $p$-Laplacian equations in a bounded domain with a variable and generally non-smooth diffusion coefficient having at most a finite number of zeroes. The main attention is focused on the case that the diffusion coefficient $a(x)$ in such equations satisfies the inequality $\liminf_{x\to z}|x-z|^{-p}a(x)> 0$ for every $ z\in \overline\Omega$. We show the existence of weak solutions and global attractors in $L^2(\Omega)$, $L^q(\Omega)$ $(q\geq 2)$ and $D_0^{1,p}(\Omega)$, respectively.

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Shan Ma. Hongtao Li. "The long-time behavior of weighted $p$-Laplacian equations." Topol. Methods Nonlinear Anal. 54 (2A) 685 - 700, 2019. https://doi.org/10.12775/TMNA.2019.064

Information

Published: 2019
First available in Project Euclid: 29 July 2019

zbMATH: 07198804
MathSciNet: MR4061316
Digital Object Identifier: 10.12775/TMNA.2019.064

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 2A • 2019
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