Comptes Rendus
Partial Differential Equations
Degenerate anisotropic variational inequalities with L1-data
[Inéquations variationnelles dégénérescents anisotropes avec données dans L1]
Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 441-444.

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 L1. 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 L1-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.

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DOI : 10.1016/j.crma.2007.09.004

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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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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