The precise boundary trace of solutions of a class of supercritical nonlinear equations

Marcus, Moshe; Véron, Laurent

doi:10.1016/j.crma.2006.11.028

Partial Differential Equations

The precise boundary trace of solutions of a class of supercritical nonlinear equations
[La trace au bord précise des solutions d'une classe d'équations non linéaires sur-critiques]

Présenté par : Haïm Brezis

Marcus, Moshe ¹ ; Véron, Laurent ²

¹ Department of Mathematics, Technion, Haifa 32000, Israel
² Laboratoire de mathématiques et physique théorique, faculté des sciences, parc de Grandmont, 37200 Tours, France

Comptes Rendus. Mathématique, Tome 344 (2007) no. 3, pp. 181-186.

Résumé
Abstract

Nous construisons et étudions les propriétés de la trace au bord précise des solutions positives de $- Δ u + u^{q} = 0$ dans un domaine régulier de $R^{N}$ , dans le cas sur-critique $q ⩾ q_{c} = (N + 1) / (N - 1)$ .

We construct and study the properties of the precise boundary trace of positive solutions of $- Δ u + u^{q} = 0$ in a smooth bounded domain of $R^{N}$ , in the supercritical case $q ⩾ q_{c} = (N + 1) / (N - 1)$ .

Accepté le : 2006-11-14
Publié le : 2006-12-21

DOI : 10.1016/j.crma.2006.11.028

Affiliations des auteurs :

Marcus, Moshe ¹ ; Véron, Laurent ²

¹ Department of Mathematics, Technion, Haifa 32000, Israel
² Laboratoire de mathématiques et physique théorique, faculté des sciences, parc de Grandmont, 37200 Tours, France

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Marcus, Moshe; Véron, Laurent. The precise boundary trace of solutions of a class of supercritical nonlinear equations. Comptes Rendus. Mathématique, Tome 344 (2007) no. 3, pp. 181-186. doi : 10.1016/j.crma.2006.11.028. http://www.numdam.org/articles/10.1016/j.crma.2006.11.028/

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