A quantitative second order minimality criterion for cavities in elastic bodies

TL;DR

This paper establishes a second order minimality criterion for cavities in elastic bodies, demonstrating that positive second variation ensures strict local minimality and providing quantitative estimates.

Contribution

It introduces a second order minimality criterion for cavities in elastic bodies and offers quantitative estimates for critical points with positive second variation.

Findings

Positive second variation implies strict local minimality.

A quantitative estimate for the minimality condition.

Theoretical validation of the minimality criterion.

Abstract

We consider a functional which models an elastic body with a cavity. We show that if a critical point has positive second variation then it is a strict local minimizer. We also provide a quantitative estimate.