Sharp estimates for the Gaussian torsional rigidity with Robin boundary conditions

TL;DR

This paper establishes sharp estimates for the Gaussian torsional rigidity under Robin boundary conditions by comparing solutions of the torsion problem for the Hermite operator with those of a symmetrized problem.

Contribution

It introduces a comparison result that links solutions of the Hermite operator's torsion problem with Robin boundary conditions to a symmetrized problem, providing new bounds.

Findings

Derived sharp estimates for Gaussian torsional rigidity.

Established a comparison principle for solutions with Robin boundary conditions.

Extended classical results to the Hermite operator context.

Abstract

In this paper we provide a comparison result between the solutions to the torsion problem for the Hermite operator with Robin boundary conditions and the one of a suitable symmetrized problem.