On the nondegeneracy of the critical points of the Robin function in symmetric domains
[Sur le non-dégénérescence des points critiques de la fonction de Robin dans les domaines symétriques]
Grossi, Massimo1
1 Dipartimento di Matematica, Università di Roma “La Sapienza” P.le Aldo Moro, 2, 00185 Roma, Italy
Comptes Rendus. Mathématique, Tome 335 (2002) no. 2, pp. 157-160.

Soit Ω un domain borné et régulier de ℝ N , N⩾2, qui est symétrique par rapport à l'origine. Dans cette Note, nous montrons que, sous certaines hypothèses sur Ω (par exemple convexité dans les directions x1,…,xN), la matrice hessienne calculée à zero est diagonale et strictement négative.

Let Ω be a smooth bounded domain of ℝ N , N⩾2, which is symmetric with respect to the origin. In this Note we prove that, under some geometrical condition on Ω (for example convexity in the directions x1,…,xN), the Hessian matrix of the Robin function computed at zero is diagonal and strictly negative definite.

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02448-2
Grossi, Massimo 1

1 Dipartimento di Matematica, Università di Roma “La Sapienza” P.le Aldo Moro, 2, 00185 Roma, Italy 
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Grossi, Massimo. On the nondegeneracy of the critical points of the Robin function in symmetric domains. Comptes Rendus. Mathématique, Tome 335 (2002) no. 2, pp. 157-160. doi : 10.1016/S1631-073X(02)02448-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02448-2/

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