Accepted Paper

Inserted: 5 nov 2020
Last Updated: 5 nov 2020

Journal: Comptes Rendus Mathematique
Year: 2018
Doi: https://doi.org/10.1016/j.crma.2018.04.012

Abstract:

We consider the classical "Serrin symmetry result" for the overdetermined boundary value problem related to the equation $\Delta u=-1$ 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.