Stability of equilibrium configurations of elastic films in two and three dimensions

TL;DR

This paper provides a criterion based on the second variation for determining local minimality of equilibrium configurations in elastic films, applicable in 2D and 3D, with implications for understanding flat morphologies.

Contribution

It extends the local minimality criterion to three-dimensional elastic films and general nonlinear energies, broadening the theoretical understanding of film stability.

Findings

Established a sufficiency criterion for local minimality based on second variation positivity.

Extended the criterion to 3D elastic films and nonlinear elastic energies.

Applied the results to analyze the stability of flat film morphologies.

Abstract

We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.