On D.Y. Gao and R.W. Ogden's paper "Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation"

TL;DR

This paper critically examines a recent claim about solutions in phase transition problems, providing counterexamples to demonstrate the claim's invalidity and clarifying the theoretical context.

Contribution

It offers a rigorous analysis and refutes a specific recent result on global minimizers and local extrema in non-convex variational problems.

Findings

The claimed result by Gao and Ogden is false.

Counter-examples disprove the original theorem.

Clarifies the theoretical context of phase transition solutions.

Abstract

In this note we prove that a recent result stated by D.Y. Gao and R.W. Ogden on global minimizers and local extrema in a phase transition problem is false. Our goal is achieved by providing a thorough analysis of the context and result in question and counter-examples.