Estimates of variational eigenvalues on metric measure spaces

TL;DR

This paper investigates variational eigenvalues on doubling metric measure spaces, establishing the existence of minimizers for Neumann eigenvalues and providing estimates for these eigenvalues.

Contribution

It proves the existence of minimizers for variational Neumann (p,q)-eigenvalues on metric measure spaces and derives estimates for these eigenvalues.

Findings

Existence of minimizers for variational Neumann (p,q)-eigenvalues.

Estimates for Neumann eigenvalues on metric measure spaces.

Results applicable to doubling metric measure spaces.

Abstract

In the article, we study variational eigenvalues on doubling metric measure spaces. We prove existence of minimizers of variational Neumann $(p,q)$-eigenvalues on metric measure spaces and on this base we obtain estimates of Neumann eigenvalues.