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.File | Dimensione | Formato | |
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