Solutions concentrating at curves for some singularly perturbed elliptic problems

Andrea Malchiodi

doi:10.1016/j.crma.2004.03.023

Partial Differential Equations

Solutions concentrating at curves for some singularly perturbed elliptic problems

Presented by: Haı̈m Brezis

Andrea Malchiodi ¹

¹ SISSA, via Beirut 2-4, 34014 Trieste, Italy

Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 775-780.

Abstract (Original language)
Résumé

We study positive solutions of the equation −ε²Δu+u=u^p, 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 $\partial Ω$ .

On étudie les solutions positives de l'équation −ε²Δu+u=u^p, 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 $\partial Ω$ .

Received: 2004-03-16
Accepted: 2004-03-16
Published online: 2004-04-09

DOI: 10.1016/j.crma.2004.03.023

Author's affiliations:

Andrea Malchiodi ¹

¹ SISSA, via Beirut 2-4, 34014 Trieste, Italy

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     title = {Solutions concentrating at curves for some singularly perturbed elliptic problems},
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Andrea Malchiodi. Solutions concentrating at curves for some singularly perturbed elliptic problems. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 775-780. doi : 10.1016/j.crma.2004.03.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.023/

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