Abstract
In this paper, we prove short time existence, uniqueness, and regularity for a surface diffusion evolution equation with curvature regularization 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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Fonseca, I., Fusco, N., Leoni, G. et al. Motion of Elastic Thin Films by Anisotropic Surface Diffusion with Curvature Regularization. Arch Rational Mech Anal 205, 425–466 (2012). https://doi.org/10.1007/s00205-012-0509-4
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DOI: https://doi.org/10.1007/s00205-012-0509-4