BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Variational Methods for Crystal Surface Instability Fonseca, Irene


Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy.\\r\\nIn addition, short time existence, uniqueness, and regularity for an\\r\\nanisotropic surface diffusion evolution equation with curvature\\r\\nregularization are proved in the context of epitaxially strained\\r\\ntwo-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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