no. 9
Partial differential equations
Solutions to a nonlinear Neumann problem in three-dimensional exterior domains
[Solutions d'un problème de Neumann non linéaire dans des domaines extérieurs de dimension 3]

Présenté par : Jean-Michel Coron

Olivier, Adélaïde1 ; Rey, Olivier2
1 Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
2 IHPST, Université Paris-1 Panthéon-Sorbonne, CNRS, 13, rue du Four, 75006 Paris, France
Comptes Rendus. Mathématique, Tome 356 (2018) no. 9, pp. 933-956.

Nous démontrons, pour un problème elliptique de Neumann avec non-linéarité presque critique, dans un domaine extérieur de dimension trois, l'existence de solutions qui se concentrent en plusieurs points de la frontière lorsque la non-linéarité devient critique.

We prove the existence of multipeak solutions to a nonlinear elliptic Neumann problem involving nearly critical Sobolev exponent, in three-dimensional exterior domains.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.07.005
Olivier, Adélaïde 1 ; Rey, Olivier 2

1 Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
2 IHPST, Université Paris-1 Panthéon-Sorbonne, CNRS, 13, rue du Four, 75006 Paris, France 
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Olivier, Adélaïde; Rey, Olivier. Solutions to a nonlinear Neumann problem in three-dimensional exterior domains. Comptes Rendus. Mathématique, Tome 356 (2018) no. 9, pp. 933-956. doi : 10.1016/j.crma.2018.07.005. http://www.numdam.org/articles/10.1016/j.crma.2018.07.005/

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