no. 10
Partial Differential Equations
Solutions concentrating at curves for some singularly perturbed elliptic problems
[Solutions se concentrant sur des courbes pour certains problèmes elliptiques singulières]

Présenté par : Haı̈m Brezis

Malchiodi, Andrea1
1 SISSA, via Beirut 2-4, 34014 Trieste, Italy
Comptes Rendus. Mathématique, Tome 338 (2004) no. 10, pp. 775-780.

On étudie les solutions positives de l'équation −ε2Δu+u=up, où p>1 et ε>0 est petit, avec conditions de Neumann sur le bord sur un domaine Ω en dimension 3. On prouve l'existence de solutions qui se concentrent le long de certaines courbes fermées de ∂Ω.

We study positive solutions of the equation −ε2Δu+u=up, where p>1 and ε>0 is small, with Neumann boundary conditions in a three-dimensional domain Ω. We prove the existence of solutions concentrating along some closed curve on ∂Ω.

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Accepté le :
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DOI : 10.1016/j.crma.2004.03.023
Malchiodi, Andrea 1

1 SISSA, via Beirut 2-4, 34014 Trieste, Italy 
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Malchiodi, Andrea. Solutions concentrating at curves for some singularly perturbed elliptic problems. Comptes Rendus. Mathématique, Tome 338 (2004) no. 10, pp. 775-780. doi : 10.1016/j.crma.2004.03.023. http://www.numdam.org/articles/10.1016/j.crma.2004.03.023/

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