[Résolubilité normale des problèmes elliptiques linéaires]
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.
Publié le :
@article{CRMATH_2002__334_6_457_0,
author = {Volpert, Vitaly and Volpert, Aizik},
title = {Normal solvability of linear elliptic problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {457--462},
publisher = {Elsevier},
volume = {334},
number = {6},
year = {2002},
doi = {10.1016/S1631-073X(02)02286-0},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02286-0/}
}
TY - JOUR AU - Volpert, Vitaly AU - Volpert, Aizik TI - Normal solvability of linear elliptic problems JO - Comptes Rendus. Mathématique PY - 2002 SP - 457 EP - 462 VL - 334 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02286-0/ DO - 10.1016/S1631-073X(02)02286-0 LA - en ID - CRMATH_2002__334_6_457_0 ER -
%0 Journal Article %A Volpert, Vitaly %A Volpert, Aizik %T Normal solvability of linear elliptic problems %J Comptes Rendus. Mathématique %D 2002 %P 457-462 %V 334 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02286-0/ %R 10.1016/S1631-073X(02)02286-0 %G en %F CRMATH_2002__334_6_457_0
Volpert, Vitaly; Volpert, Aizik. Normal solvability of linear elliptic problems. Comptes Rendus. Mathématique, Tome 334 (2002) no. 6, pp. 457-462. doi : 10.1016/S1631-073X(02)02286-0. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02286-0/
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