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

Bellettini, G.; Novaga, M.; Paolini, M.

Interfaces Free Bound. 3, No. 4, 415-446 (2001).

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.

MSC:

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

Keywords:

crystalline mean curvature; anisotropic evolutions; calibrable facet