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Epitaxially strained elastic films: the case of anisotropicsurface energies

Published online by Cambridge University Press:  01 March 2012

Marco Bonacini
Marco Bonacini*
Affiliation:
SISSA, Via Bonomea 265, 34136 Trieste, Italy. mbonacin@sissa.it
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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 determinationof equilibrium configurations. We show that the threshold effect that describes thestability 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 showthat the flat configuration is always a local minimizer of the total energy. Following theapproach of [N. Fusco and M. Morini, Equilibrium configurations of epitaxially strainedelastic films: second order minimality conditions and qualitative properties of solutions.Preprint], we obtain these results by means of a minimality criterion based on thepositivity of the second variation.

Keywords

Epitaxially strained crystalline filmsanisotropic surface energysecond order minimality conditionssecond variation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 167 - 189
Copyright
© EDP Sciences, SMAI, 2012

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