Computing the first eigenpair for problems with variable exponents

TL;DR

This paper computes the first eigenpair for variable exponent eigenvalue problems, compares different definitions of the first eigenvalue, and discusses symmetry breaking phenomena.

Contribution

It introduces a method to compute the first eigenpair for variable exponent problems and compares homogeneous and nonhomogeneous eigenvalue notions.

Findings

Comparison of homogeneous and nonhomogeneous eigenvalues

Identification of symmetry breaking phenomena

Method for computing the first eigenpair

Abstract

We compute the first eigenpair for variable exponent eigenvalue problems. We compare the homogeneous definition of first eigenvalue with previous nonhomogeneous notions in the literature. We highlight the symmetry breaking phenomena