Comptes Rendus
no. 6
Partial differential equations/Differential geometry
A Serrin-type symmetry result on model manifolds: An extension of the Weinberger argument

Presented by: Haïm Brézis

Alberto Roncoroni1
1 Dipartimento di Matematica F. Casorati, Università degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 648-656.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.04.012

Alberto Roncoroni 1

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

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