On the location of two blowup points on an annulus for the mean field equation

Grossi, Massimo; Takahashi, Futoshi

doi:10.1016/j.crma.2014.04.006

Partial differential equations

On the location of two blowup points on an annulus for the mean field equation
[Sur l'emplacement de deux points d'explosion sur un annulus pour l'équation de champ moyen]

Présenté par : Haïm Brézis

Grossi, Massimo ¹ ; Takahashi, Futoshi ²

¹ Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le Aldo Moro 2, 00185 Roma, Italy
² Department of Mathematics, Osaka City University & OCAMI, Sumiyoshi-ku, Osaka 558-8585, Japan

Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 615-619.

Résumé
Abstract

Nous considérons l'équation de champ moyen sur les domaines annulaires à deux dimensions, et prouvons que, si $P_{1}$ et $P_{2}$ sont deux points d'explosion, alors nous devons avoir $P_{1} = - P_{2}$ .

We consider the mean field equation on two-dimensional annular domains, and prove that if $P_{1}$ and $P_{2}$ are two blowup points of a blowing-up solution sequence of the equation, then we must have $P_{1} = - P_{2}$ .

Reçu le : 2014-02-25
Accepté le : 2014-04-15
Publié le : 2014-06-27

DOI : 10.1016/j.crma.2014.04.006

Affiliations des auteurs :

Grossi, Massimo ¹ ; Takahashi, Futoshi ²

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Grossi, Massimo; Takahashi, Futoshi. On the location of two blowup points on an annulus for the mean field equation. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 615-619. doi : 10.1016/j.crma.2014.04.006. http://www.numdam.org/articles/10.1016/j.crma.2014.04.006/

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