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.
A Serrin-type symmetry result on model manifolds: An extension of the Weinberger argument
Roncoroni A.
2018-01-01
Abstract
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.File in questo prodotto:
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