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arXiv · 2212.05375

On a reverse Kohler-Jobin inequality

Luca Briani·Giuseppe Buttazzo·Serena Guarino Lo Bianco
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Abstract

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 {\it nearly spherical domains}.

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Luca Briani, Giuseppe Buttazzo, Serena Guarino Lo Bianco. 2022-12-10. On a reverse Kohler-Jobin inequality. https://arxiv.org/abs/2212.05375

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