Optimal domains for the Cheeger inequality

Dorin Bucur, Giuseppe Buttazzo, Alexis de Villeroché

In this paper we consider the scale invariant shape functional $${\mathcal{F}}_{p,q}(\hat{I}\text{c◯})=\frac{\hat{I}{»}_p^{1/p}(\hat{I}\text{c◯})}{\hat{I}{»}_q^{1/q}(\hat{I}\text{c◯})},$$ where $1\le q<p\le +\infty$ and $\hat{I}{»}_p(\hat{I}\text{c◯})$ (respect…