Degenerate anisotropic variational inequalities with $ {L}^{1}$-data

Alexander A. Kovalevsky; Yuliya S. Gorban

doi:10.1016/j.crma.2007.09.004

Partial Differential Equations

Degenerate anisotropic variational inequalities with

L^{1}

-data
[Inéquations variationnelles dégénérescents anisotropes avec données dans

L^{1}

]

Présenté par : Philippe G. Ciarlet

Alexander A. Kovalevsky ¹ ; Yuliya S. Gorban ²

¹ Institute of Applied Mathematics and Mechanics, Rosa Luxemburg St. 74, 83114 Donetsk, Ukraine
² Donetsk National University, Universitetskaya St. 24, 83055 Donetsk, Ukraine

Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 441-444.

Résumé
Abstract

Dans cette Note nous introduisons les notions de T-solution et T-solution translatante des inéquations variationnelles correspondant à un opérateur non linéair dégénérescent anisotrope elliptique, un ensemble de contraintes d'une classe suffisament large et le second membre dans $L^{1}$ . Nous donnons les théorèmes d'existence, d'unicité et de propriétées de ces solutions et décrivons leur relation avec solutions des inéquations variationnelles au sens ordinaire.

In this Note we introduce notions of T-solution and shift T-solution of variational inequalities corresponding to a nonlinear degenerate anisotropic elliptic operator, a set of constraints of a sufficiently large class and an $L^{1}$ -right-hand side. We give theorems on the existence, uniqueness and properties of these solutions and describe their relation with solutions of variational inequalities in usual sense.

Reçu le : 2007-05-23
Accepté le : 2007-09-12
Publié le : 2007-10-15

DOI : 10.1016/j.crma.2007.09.004

Affiliations des auteurs :

Alexander A. Kovalevsky ¹ ; Yuliya S. Gorban ²

¹ Institute of Applied Mathematics and Mechanics, Rosa Luxemburg St. 74, 83114 Donetsk, Ukraine
² Donetsk National University, Universitetskaya St. 24, 83055 Donetsk, Ukraine

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     title = {Degenerate anisotropic variational inequalities with $ {L}^{1}$-data},
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Alexander A. Kovalevsky; Yuliya S. Gorban. Degenerate anisotropic variational inequalities with $ {L}^{1}$-data. Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 441-444. doi : 10.1016/j.crma.2007.09.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.004/

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Nina V. Kasimova Solvability issue for optimal control problem in coefficients for degenerate parabolic variational inequality, Contemporary approaches and methods in fundamental mathematics and mechanics, Cham: Springer, 2021, pp. 457-473 | DOI:10.1007/978-3-030-50302-4_22 | Zbl:1478.49007
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