We 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.

A general integral identity with applications to a reverse Serrin problem / Rolando Magnanini. - In: JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1559-002X. - STAMPA. - 34:(2024), pp. 244.1-244.26. [10.1007/s12220-024-01693-8,]

A general integral identity with applications to a reverse Serrin problem

Rolando Magnanini
2024

Abstract

We 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.
2024
34
1
26
Rolando Magnanini
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1359493
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