Some shape functionals for the $k$-Hessian equation
Analysis of PDEs
2025-09-26 v1
Abstract
For a non-empty, bounded, open, and convex set of class , we consider the Torsional Rigidity associated to the -Hessian operator. We first prove P\'olya type lower bound for the -Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the P\'olya type inequality, we provide two quantitative estimates.
Cite
@article{arxiv.2509.21313,
title = {Some shape functionals for the $k$-Hessian equation},
author = {Alba Lia Masiello and Francesco Salerno},
journal= {arXiv preprint arXiv:2509.21313},
year = {2025}
}