Abstract
We consider a variational model introduced in the physical literature to describe the epitaxial growth of an elastic film over a thick flat substrate when a lattice mismatch between the two materials is present. We study quantitative and qualitative properties of equilibrium configurations, that is, of local and global minimizers of the free-energy functional. More precisely, we determine analytically the critical threshold for the local minimality of the flat configuration and we also prove several results concerning its global minimality. The non-occurrence of singularities in non-flat global minimizers is also addressed. One of the main results of the paper is a new sufficient condition for local minimality, which provides the first extension of the classical criteria based on the positivity of the second variation to the context of functionals with bulk and surface energies.
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Fusco, N., Morini, M. Equilibrium Configurations of Epitaxially Strained Elastic Films: Second Order Minimality Conditions and Qualitative Properties of Solutions. Arch Rational Mech Anal 203, 247–327 (2012). https://doi.org/10.1007/s00205-011-0451-x
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DOI: https://doi.org/10.1007/s00205-011-0451-x