Partial Differential Equations
Boundary singularities of positive solutions of some nonlinear elliptic equations
Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 83-88.

We study the behavior near x0 of any positive solution of (E) Δu=uq in Ω which vanishes on Ω{x0}, where ΩRN is a smooth domain, q(N+1)/(N1) and x0Ω. Our results are based upon a priori estimates of solutions of (E) and existence, non-existence and uniqueness results for solutions of some nonlinear elliptic equations on the upper-half unit sphere.

Nous étudions le comportement quand x tend vers x0 de toute solution positive de (E) Δu=uq dans Ω qui s'annule sur Ω{x0}, où ΩRN est un domaine régulier, q(N+1)/(N1) et x0Ω. Nos résultats sont fondés sur des estimations a priori des solutions de (E), et des résultats d'existence, de non existence et d'unicité de solutions de certaines équations elliptiques non linéaires sur la demi-sphère unité.

Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.027
Bidaut-Véron, Marie-Françoise 1; Ponce, Augusto C. 1; Véron, Laurent 1

1 Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Faculté des Sciences, 37200 Tours, France
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Bidaut-Véron, Marie-Françoise; Ponce, Augusto C.; Véron, Laurent. Boundary singularities of positive solutions of some nonlinear elliptic equations. Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 83-88. doi : 10.1016/j.crma.2006.11.027. http://www.numdam.org/articles/10.1016/j.crma.2006.11.027/

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