[Sur le non-dégénérescence des points critiques de la fonction de Robin dans les domaines symétriques]
Soit un domain borné et régulier de , N⩾2, qui est symétrique par rapport à l'origine. Dans cette Note, nous montrons que, sous certaines hypothèses sur (par exemple convexité dans les directions x1,…,xN), la matrice hessienne calculée à zero est diagonale et strictement négative.
Let be a smooth bounded domain of , N⩾2, which is symmetric with respect to the origin. In this Note we prove that, under some geometrical condition on (for example convexity in the directions x1,…,xN), the Hessian matrix of the Robin function computed at zero is diagonal and strictly negative definite.
Publié le :
Massimo Grossi 1
@article{CRMATH_2002__335_2_157_0, author = {Massimo Grossi}, title = {On the nondegeneracy of the critical points of the {Robin} function in symmetric domains}, journal = {Comptes Rendus. Math\'ematique}, pages = {157--160}, publisher = {Elsevier}, volume = {335}, number = {2}, year = {2002}, doi = {10.1016/S1631-073X(02)02448-2}, language = {en}, }
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/
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