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Irene Fonseca\\
Carnegie Mellon University\\
Department of Mathematical Sciences\\
Carnegie Mellon Univeristy \\
Pittsburgh, PA  15213\\
fonseca@andrew.cmu.edu\\

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Giovanni Leoni\\
Carnegie Mellon University\\
Department of Mathematical Sciences\\
Carnegie Mellon Univeristy \\
Pittsburgh, PA  15213\\
giovanni@andrew.cmu.edu\\

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Nicola Fusco\\
Dipartimento di Matematica e Applicazioni ``R. Caccioppoli''\\
Universit\`a degli Studi di Napoli ``Federico II''\\
Napoli, Italy\\
n.fusco@unina.it

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and 

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Massamiliano Morini\\
SISSA\\
Trieste, Italy\\
morini@sissa.it
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\noindent{\bf Abstract}.  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, the 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 by product, to a rigorous proof of the zero contact-angle condition
between islands and wetting layers.

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