The Cheeger N-problem in terms of BV functions

TL;DR

This paper reformulates the Cheeger N partition problem using BV functions, providing a new existence proof and exploring connections to the second eigenvalue of the 1-Laplace operator.

Contribution

It introduces a BV function-based formulation for the Cheeger N problem and establishes links to spectral properties of the 1-Laplace operator.

Findings

New existence proof for the Cheeger-N problem

Connection between Cheeger-2 problem and second eigenvalue of 1-Laplace operator

Reformulation facilitates analysis of partition problems

Abstract

We reformulate the Cheeger N partition problem as a minimization among a suitable class of BV functions. This allows us to obtain a new existence proof for the Cheeger-N-problem. Moreover, we derive some connections between the Cheeger-2- problem and the second eigenvalue of the 1-Laplace operator.