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Publication 11-CNA-002

Motion of Elastic Thin Films by Anisotropic Surface Diffusion with Curvature Regularization

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

Nicola Fusco
University of Napoli
Naples, Italy
nfusco@unina.it

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

Massimiliano Morini
SISSA
Trieste, Italy
morini@sissa.it

Abstract: Short time existence, uniqueness, and regularity for a surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the H-1-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

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