Inserted: 12 jul 2011
Last Updated: 9 feb 2013
Journal: ESAIM Control Optim. Calc. Var.
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.