Elliptic equations in dimension three: a conjecture of H. Brezis
[Equations elliptiques en dimension 3 : une conjecture de H. Brezis]
Druet, Olivier1
1 Département de mathématiques, Université de Cergy-Pontoise, site de Saint-Martin, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 643-647.

On étudie l'existence de solutions minimisantes à une EDP elliptique à croissance de Sobolev critique sur des domaines de l'espace euclidien de dimension trois. On résout en particulier une conjecture de H. Brezis sur le sujet. Les questions analogues en dimensions plus grandes étaient parfaitement comprises depuis des travaux de H. Brezis et L. Nirenberg.

We study the existence of minimizing solutions for an elliptic equation involving critical Sobolev exponent on domains of the three-dimensional Euclidean space. We solve in particular by the affirmative a conjecture of Haı̈m Brezis. The similar situation in higher dimensions was completely understood thanks to previous works by H. Brezis and L. Nirenberg.

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02289-6
Druet, Olivier 1

1 Département de mathématiques, Université de Cergy-Pontoise, site de Saint-Martin, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France 
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Druet, Olivier. Elliptic equations in dimension three: a conjecture of H. Brezis. Comptes Rendus. Mathématique, Tome 334 (2002) no. 8, pp. 643-647. doi : 10.1016/S1631-073X(02)02289-6. http://www.numdam.org/articles/10.1016/S1631-073X(02)02289-6/

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