# On a class of Cheeger inequalities

created by buttazzo on 25 Nov 2021

[BibTeX]

Preprint

Inserted: 25 nov 2021
Last Updated: 25 nov 2021

Year: 2021

Abstract:

We study a general version of the Cheeger inequality by considering the shape functional ${\mathcal F}_{p,q}(\Omega)=\lambda_p^{1/p}(\Omega)/\lambda_q(\Omega)^{1/q}$. The infimum and the supremum of ${\mathcal F}_{p,q}$ are studied in the class of {\it all} domains $\Omega$ of ${\mathbb R}^d$ and in the subclass of {\it convex} domains. In the latter case the issue concerning the existence of an optimal domain for ${\mathcal F}_{p,q}$ is discussed.