Comptes Rendus
no. 6
Normal solvability of linear elliptic problems
[Résolubilité normale des problèmes elliptiques linéaires]
Vitaly Volpert1 ; Aizik Volpert2
1 Mathématiques appliquées, UMR 5585 CNRS, Université Lyon 1, 69622 Villeurbanne, France
2 Department of Mathematics, Technion, 32000 Haifa, Israel
Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 457-462.

L'article est consacré aux problèmes elliptiques générals. Nous considérons des domaines non bornés et les espaces de Hölder. On définit les problèmes limites à l'infinie ce qui permet de formuler la condition nécessaire et suffisante de la résolubilité normale. Nous étudions la structure de l'espace dual et décrivons le sous-espace de fonctionnelles qui déterminent les conditions de resolubilité. Cela nous permet de démontrer que pour les opérateurs de Fredholm, tous les problèmes limites sont inversibles.

The paper is devoted to general linear elliptic problems in Hölder spaces. We consider unbounded domains and define limiting problems at infinity. We give a necessary and sufficient condition of normal solvability through uniqueness of solutions of limiting problems. We study a structure of spaces dual to Hölder spaces and specify the subspace of functionals, which provide the condition of normal solvability. This allows us to prove that for Fredholm operators all limiting operators are invertible.

Reçu le :
Publié le :
DOI : 10.1016/S1631-073X(02)02286-0
Vitaly Volpert 1 ; Aizik Volpert 2

1 Mathématiques appliquées, UMR 5585 CNRS, Université Lyon 1, 69622 Villeurbanne, France
2 Department of Mathematics, Technion, 32000 Haifa, Israel 
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Vitaly Volpert; Aizik Volpert. Normal solvability of linear elliptic problems. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 457-462. doi : 10.1016/S1631-073X(02)02286-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02286-0/

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[6] S.A. Nazarov; K. Pileckas On the Fredholm property of the Stokes operator in a layer-like domain, J. Anal. Appl., Volume 20 (2001) no. 1, pp. 155-182

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[8] V. Volpert; A. Volpert; J.F. Collet Topological degree for elliptic operators in unbounded cylinders, Adv. Differential Equations, Volume 4 (1999) no. 6, pp. 777-812

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