# Science at the triple point between mathematics, mechanics and materials science

## Publication 72

### Motion of Three-Dimensional Elastic Films by Anisotropic Surface Diffusion with Curvature Regularization

##### Authors:

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Nicola Fusco
Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Universita degli Studi di Napoli "Federico II"
Napoli, Italy

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

M. Morini
Dipartimento di Matematica
Universita degli Studi di Parma
Parma, Italy

##### Abstract:
Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^1$-gradient low structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a at configuration are also addressed.
##### Get the paper in its entirety
14-CNA-012.pdf

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