# On functionals involving the torsional rigidity related to some classes of nonlinear operators

## TL;DR

This paper investigates optimal bounds for anisotropic p-torsional rigidity functionals, relating geometric properties of domains to torsional measures, extending understanding of nonlinear operator effects on shape optimization.

## Contribution

It introduces new estimates for functionals involving anisotropic p-torsional rigidity, connecting geometric domain features with nonlinear operator properties.

## Key findings

- Derived bounds for $rac{T_p(
abla)}{|
abla| M(
abla)}$
- Established relationships between torsional rigidity and anisotropic inradius
- Provided insights into nonlinear operator effects on domain functionals

## Abstract

In this paper we study optimal estimates for two functionals involving the anisotropic $p$-torsional rigidity $T_p(\Omega)$, $1<p<+\infty$. More precisely, we study $\Phi(\Omega)=\frac{T_p(\Omega)}{|\Omega|M(\Omega)}$ and $\Psi(\Omega)=\frac{T_p(\Omega)}{|\Omega|[R_{F}(\Omega)]^{\frac{p}{p-1}}}$, where $M(\Omega)$ is the maximum of the torsion function $u_{\Omega}$ and $R_F(\Omega)$ is the anisotropic inradius of $\Omega$.