A quantitative Talenti-type comparison result with Robin boundary conditions
Analysis of PDEs
2025-11-17 v1
Abstract
The purpose of this paper is to establish a quantitative version of the Talenti comparison principle for solutions to the Poisson equation with Robin boundary conditions. This quantitative enhancement is proved in terms of the asymmetry of domain. The key role is played by a careful analysis of the propagation of asymmetry for the level sets of the solutions of a PDE. As a byproduct, we obtain an alternative proof of the quantitative Saint-Venant inequality for the Robin torsion and, in the planar case, of the quantitative Faber-Krahn inequality for the first Robin eigenvalue. In addition, we complete the framework of the rigidity result of the Talenti inequalities with Robin boundary conditions.
Keywords
Cite
@article{arxiv.2511.11316,
title = {A quantitative Talenti-type comparison result with Robin boundary conditions},
author = {Vincenzo Amato and Rosa Barbato and Simone Cito and Alba Lia Masiello and Gloria Paoli},
journal= {arXiv preprint arXiv:2511.11316},
year = {2025}
}