On nondegeneracy of solutions to $ \mathit{SU}(3)$ Toda system

Wei, Juncheng; Zhao, Chunyi; Zhou, Feng

doi:10.1016/j.crma.2010.11.025

Partial Differential Equations

On nondegeneracy of solutions to

SU (3)

Toda system
[Sur la nondégénérescence de solutions de

SU (3)

système de Toda]

Présenté par : Haïm Brezis

Wei, Juncheng ¹ ; Zhao, Chunyi ² ; Zhou, Feng ²

¹ Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
² Department of Mathematics, East China Normal University, Shanghai, 200241, PR China

Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 185-190.

Résumé
Abstract

On montre que pour toute solution de $SU (3)$ système de Toda suivant $Δ u + 2 e^{u} - e^{v} = 0$ , $Δ v - e^{u} + 2 e^{v} = 0$ dans $R^{2}$ , $\int_{R^{2}} e^{u} < \infty$ , $\int_{R^{2}} e^{v} < \infty$ , le noyau de l'opérateur linéarisé associé est exactement de dimension huit, i.e., ce qu'on appelle la nondégénérescence.

We prove that the solution to the following $SU (3)$ Toda system

{\begin{matrix} Δ u + 2 e^{u} - e^{v} = 0, Δ v - e^{u} + 2 e^{v} = 0 in R^{2}, \\ \int_{R^{2}} e^{u} < \infty, \int_{R^{2}} e^{v} < \infty, \end{matrix}

is nondegenerate, i.e., the kernel of the associated linearized operator is exactly eight-dimensional.

Reçu le : 2010-11-23
Publié le : 2011-01-12

DOI : 10.1016/j.crma.2010.11.025

Affiliations des auteurs :

Wei, Juncheng ¹ ; Zhao, Chunyi ² ; Zhou, Feng ²

¹ Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
² Department of Mathematics, East China Normal University, Shanghai, 200241, PR China

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     title = {On nondegeneracy of solutions to $ \mathit{SU}(3)$ {Toda} system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {185--190},
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     doi = {10.1016/j.crma.2010.11.025},
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Wei, Juncheng; Zhao, Chunyi; Zhou, Feng. On nondegeneracy of solutions to $ \mathit{SU}(3)$ Toda system. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 185-190. doi : 10.1016/j.crma.2010.11.025. http://www.numdam.org/articles/10.1016/j.crma.2010.11.025/

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