Calculus of Variations and Geometric Measure Theory

M. Bonacini

Epitaxially strained elastic films: the case of anisotropic surface energies

created by bonacini on 12 Jul 2011
modified on 09 Feb 2013


Published Paper

Inserted: 12 jul 2011
Last Updated: 9 feb 2013

Journal: ESAIM Control Optim. Calc. Var.
Volume: 19
Number: 1
Pages: 167-189
Year: 2013
Doi: 10.1051/cocv/2012003


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. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.