Characterization of facet breaking for nonsmooth mean curvature flow in the convex case. (English) Zbl 0989.35127

Summary: We investigate the breaking and bending phenomena of a facet of a three-dimensional crystal which evolves under crystalline mean curvature flow. We give necessary and sufficient conditions for a facet to be calibrable, i.e. not to break or bend under the evolution process. We also give a criterion which allows us to predict exactly where a subdivision of a non-calibrable facet takes place in the evolution process.


35Q72 Other PDE from mechanics (MSC2000)
35R35 Free boundary problems for PDEs
74E15 Crystalline structure
82D25 Statistical mechanics of crystals
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