A general integral identity with applications to a reverse Serrin problem
Analysis of PDEs
2024-05-16 v2
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.
Cite
@article{arxiv.2402.02845,
title = {A general integral identity with applications to a reverse Serrin problem},
author = {Rolando Magnanini and Riccardo Molinarolo and Giorgio Poggesi},
journal= {arXiv preprint arXiv:2402.02845},
year = {2024}
}