Comptes Rendus
Partial Differential Equations
Existence via compactness for maximal monotone elliptic operators
Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 489-492.

In this Note we propose a new method of proving the existence of solutions to divA(x,u)f, when A(x,u) has x-dependent maximal monotone graph. The idea is based on the theory of Young measures and on the method of compensated compactness. Alternative approaches were proposed elsewhere. However, our method allows us to obtain also the strong convergence of approximate solutions.

Dans cette Note nous proposons une méthode nouvelle de démonstation de l'existence de solutions de divA(x,u)f, où A(x,u) a un graphe maximale monotone dépendant de x. L'idée de cette méthode est d'utiliser la théorie des mésures de Young et la méthode de compacticité par compensation. Une autre approche a été proposée ailleurs. Néanmoins, notre méthode permet d'obtenir la convergence forte des solutions approchées.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2005.02.017

Piotr Gwiazda 1; Anna Zatorska-Goldstein 1

1 Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
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Piotr Gwiazda; Anna Zatorska-Goldstein. Existence via compactness for maximal monotone elliptic operators. Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 489-492. doi : 10.1016/j.crma.2005.02.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.02.017/

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