Optimal domains for the Cheeger inequality

Dorin Bucur, Giuseppe Buttazzo, Alexis de Villeroché

In this paper we consider the scale invariant shape functional $${\mathcal{F}}_{p,q}(\Omega )=\frac{{\lambda }_p^{1/p}(\Omega )}{{\lambda }_q^{1/q}(\Omega )},$$ where $1\le q<p\le +\infty$ and ${\lambda }_p(\Omega )$ (respectively $…