Abstract
AbstractWe prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously proved and used to obtain quantitative estimates of spherical symmetry for the Serrin overdetermined boundary value problem. As an application, we prove a quantitative symmetry result for the reverse Serrin problem, which we introduce for the first time in this paper. In passing, we obtain a rigidity result for solutions of the aforementioned Poisson equation subject to a constant Neumann condition.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Università Ca’ Foscari Venezia
Australian Research Council
Australian Academy of Science
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Firenze
Publisher
Springer Science and Business Media LLC
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