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Comptes Rendus Mathématique
Volume 345, n° 8
pages 441-444 (octobre 2007)
Doi : 10.1016/j.crma.2007.09.004
Received : 23 May 2007 ;  accepted : 12 September 2007
Degenerate anisotropic variational inequalities with  -data
Inéquations variationnelles dégénérescents anisotropes avec données dans  

Alexander A. Kovalevsky a, 1 , Yuliya S. Gorban b
a Institute of Applied Mathematics and Mechanics, Rosa Luxemburg St. 74, 83114 Donetsk, Ukraine 
b Donetsk National University, Universitetskaya St. 24, 83055 Donetsk, Ukraine 


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  -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. To cite this article: A.A. Kovalevsky, Y.S. Gorban, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.

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 dʼune classe suffisament large et le second membre dans  . Nous donnons les théorèmes dʼexistence, dʼunicité et de propriétées de ces solutions et décrivons leur relation avec solutions des inéquations variationnelles au sens ordinaire. Pour citer cet article : A.A. Kovalevsky, Y.S. Gorban, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.
1  Partly supported by INTAS Project No. 05-1000008-7921.

© 2007  Académie des sciences@@#104156@@
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