Inserted: 10 aug 2017
Last Updated: 10 aug 2017
A variational model for epitaxially-strained thin films on substrates is derived both by $\Gamma$-convergence from a transition-layer setting, and by relaxation of a sharp-interface description. The model is characterized by a configurational energy that accounts for possibly different elastic properties for the film and the substrate, as well as for the surface tensions of all three involved interfaces: film-gas, substrate-gas, and film-substrate. Minimal configurations of this energy are then shown to exist and their regularity and geometrical properties are studied. The Young-Dupré law is shown to be satisfied by the angle that energetically-optimal profiles form at contact points with the substrate. This appears to be the first analytical validation of such relation, which was originally formulated in Fluid Mechanics, in the context of Continuum Mechanics for a thin-film model.