TY - JOUR T1 - Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results JF - Arch. Ration. Mech. Anal. 186 (2007) 477-537 Y1 - 2007 A1 - Irene Fonseca A1 - Nicola Fusco A1 - Giovanni Leoni A1 - Massimiliano Morini AB - 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 unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which 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. UR - http://hdl.handle.net/1963/2350 U1 - 1666 U2 - Mathematics U3 - Functional Analysis and Applications ER -