Failure of a Brunn-Minkowski-type inequality for the Gaussian torsional rigidity

Xuan Hien Nguyen, Alina Stancu

Let $u$ be the torsion function for the Ornstein-Uhlenbeck operator on a bounded domain $\Omega \subset {\mathbb{R}}^n$, i.e., the solution of $\Delta u-x\cdot \nabla u=-1$ in $\Omega$ with $u =…