Calculus of Variations and Geometric Measure Theory

P. Bella - M. Goldman - B. Zwicknagl

Study of island formation in epitaxially strained films on unbounded domains

created by goldman on 17 Feb 2014
modified on 20 Mar 2015


Accepted Paper

Inserted: 17 feb 2014
Last Updated: 20 mar 2015

Journal: ARMA
Year: 2014


We consider a variational model for the formation of islands in heteroepitaxial growth on unbounded domains. We first derive the scaling regimes of the minimal energy in terms of the volume of the film and the amplitude of the crystallographic misfit. For small volumes, non-existence of minimizers is then proven. This corresponds to the experimentally observed wetting effect. On the other hand, we show the existence of minimizers for large volumes. We finally study the asymptotic behavior of the optimal shapes.