Calculus of Variations and Geometric Measure Theory
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M. F. Bidaut-VĂ©ron - Q. H. Nguyen

Stability properties for quasilinear parabolic equations with measure data

created by nguyen on 22 Jul 2018

[BibTeX]

Published Paper

Inserted: 22 jul 2018
Last Updated: 22 jul 2018

Journal: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Pages: 33
Year: 2015
Doi: http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=9&rank=2

Abstract:

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We study problems of the model type $u_{t}-{\Delta_{p}}u=\mu$ in $Q$ $u=0$ on$\partial\Omega\times(0,T)$, $u(0)=u_{0}$ in $\Omega$ where $p>1$, $\mu\in\mathcal{M}_{b}(Q)$ and $u_{0}\in L^{1}(\Omega).$ Our main result is a \textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u\longmapsto\mathcal{A}(u)=$div$(A(x,t,\nabla u))$


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