no. 6
Partial differential equations/Differential geometry
A Serrin-type symmetry result on model manifolds: An extension of the Weinberger argument
[Un résultat de symétrie de type Serrin pour les variétés modèles : une extension de l'argument de Weinberger]

Présenté par : Haïm Brézis

Roncoroni, Alberto1
1 Dipartimento di Matematica F. Casorati, Università degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy
Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 648-656.

Nous considérons le résultat classique de « symétrie de Serrin » pour les problèmes à valeurs à la frontière surdéterminés, pour l'équation Δu=−1 sur une variété modèle de courbure de Ricci positive ou nulle. Utilisant une extension de l'argument également classique de Weinberger, nous montrons un résultat de symétrie euclidienne sous une hypothèse de « compatibilité » entre la solution et la géométrie du modèle.

We consider the classical ‘‘Serrin's symmetry result” for the overdetermined boundary value problem related to the equation Δu=−1 in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable ‘‘compatibility” assumption between the solution and the geometry of the model.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.04.012
Roncoroni, Alberto 1

1 Dipartimento di Matematica F. Casorati, Università degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy 
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Roncoroni, Alberto. A Serrin-type symmetry result on model manifolds: An extension of the Weinberger argument. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 648-656. doi : 10.1016/j.crma.2018.04.012. http://archive.numdam.org/articles/10.1016/j.crma.2018.04.012/

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