Comptes Rendus
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]
Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 157-160.

Soit Ω un domain borné et régulier de 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 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

Massimo Grossi 1

1 Dipartimento di Matematica, Università di Roma “La Sapienza” P.le Aldo Moro, 2, 00185 Roma, Italy
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02448-2/

[1] A. Bahri; Y.Y. Li; O. Rey On a variational problemwith lack of compactness: the topological effect of the critical points at infinity, Calc. Var., Volume 3 (1995), pp. 67-93

[2] C. Bandle; M. Flucher Harmonic radius and concentration of energy; hyperbolic radius and Liouville's equations, SIAM Rev., Volume 38 (1996), pp. 239-255

[3] H. Brezis; L. Peletier Asymptotics for elliptic equations involving the critical growth, Partial Differential Equations and Calculus of Variations, Progr. Nonlinear Differential Equations Appl., 1, Birkäuser, Boston, 1989, pp. 149-192

[4] D. Gilbarg; N. Trudinger Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983

[5] L. Glangetas Uniqueness of positive solutions of a nonlinear elliptic equation involving the critical exponent, Nonlinear Anal., Volume 20 (1993), pp. 571-603

[6] Z.C. Han Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponents, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 8 (1991), pp. 159-174

[7] O. Rey The role of the Green's function in a nonlinear elliptic equation involving critical Sobolev exponent, J. Funct. Anal., Volume 89 (1990), pp. 1-52

[8] O. Rey Proof of two conjecture of H. Brezis and L.A. Peletier, Manuscripta Math., Volume 65 (1989), pp. 19-37

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