Inserted: 10 aug 2017
Last Updated: 4 sep 2020
We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films identified by the authors in the companion paper Davoli, Piovano, arXiv1809.07128. The regularity of energetically-optimal film profiles is studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film and gas, substrate and gas, and film and substrate. Finally, geometrical conditions are provided for the optimal wetting angle, i.e., the angle formed at the contact point of films with the substrate. In particular, the Young-Dupré law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics.