High-order Cheeger's inequality on domain

TL;DR

This paper explores the connection between higher order eigenvalues of the p-Laplacian and Cheeger constants on domains, providing asymptotic analysis and a high-order Cheeger's inequality using domain decomposition methods.

Contribution

It introduces a novel high-order Cheeger's inequality for the p-Laplacian on domains and analyzes the asymptotic behavior of higher order Cheeger constants.

Findings

Asymptotic behavior of the k-th Cheeger constant analyzed.

High-order Cheeger's inequality established for p-Laplacian.

Domain decomposition methods used to derive inequalities.

Abstract

We study the relationship of higher order variational eigenvalues of p-Laplacian and the higher order Cheeger constants. The asymptotic behavior of the k-th Cheeger constant is investigated. Using methods of decompostion of the domain with respect to the eigenfunctions, we obtain the high-order Cheeger's inequality of p-Laplacian on domain.