Comptes Rendus
no. 2
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]
Massimo Grossi1
1Dipartimento di Matematica, Università di Roma “La Sapienza” P.le Aldo Moro, 2, 00185 Roma, Italy
Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 157-160

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.

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.

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

Massimo Grossi  1

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