Calculus of Variations and Geometric Measure Theory

L. Briani - G. Buttazzo - S. Guarino Lo Bianco

On a reverse Kohler-Jobin inequality

created by guarinolo on 10 Dec 2022


Submitted Paper

Inserted: 10 dec 2022
Last Updated: 10 dec 2022

Year: 2022


We consider the shape optimization problems for the quantities $\lambda(\Omega)T^q(\Omega)$, where $\Omega$ varies among open sets of $\mathbb{R}^d$ with a prescribed Lebesgue measure. While the characterization of the infimum is completely clear, the same does not happen for the maximization in the case $q>1$. We prove that for $q$ large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among italics nearly spherical domains.