ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - January 2013 - Volume 19, Issue 01  

Research Article

Epitaxially strained elastic films: the case of anisotropic surface energies

Marco Bonacini

SISSA, Via Bonomea 265, 34136 Trieste, Italy. mbonacin@sissa.it

Abstract

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. Following the approach of [N. Fusco and M. Morini, Equilibrium configurations of epitaxially strained elastic films: second order minimality conditions and qualitative properties of solutions. Preprint], we obtain these results by means of a minimality criterion based on the positivity of the second variation.

(Received June 22 2011)

(Online publication March 1 2012)

Key Words:

  • Epitaxially strained crystalline films;
  • anisotropic surface energy;
  • second order minimality conditions;
  • second variation

Mathematics Subject Classification:

  • 74G55;
  • 74K35;
  • 74G65;
  • 49Q20;
  • 49K10