## Publication 3

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

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##### 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*-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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