Calculus of Variations and Geometric Measure Theory

I. Fonseca - N. Fusco - G. Leoni - M. Morini

Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results

created by leoni on 30 Dec 2006
modified on 27 Jul 2011


Published Paper

Inserted: 30 dec 2006
Last Updated: 27 jul 2011

Journal: Arch. Ration. Mech. Anal.
Volume: 186
Number: 3
Pages: 477-537
Year: 2007


Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavourable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup where the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero contact-angle condition between islands and wetting layers.