Calculus of Variations and Geometric Measure Theory
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G. Bellettini - M. Novaga - G. Riey

First variation of anisotropic energies and crystalline mean curvature for partitions

created on 04 Nov 2002
modified on 17 Dec 2003


Published Paper

Inserted: 4 nov 2002
Last Updated: 17 dec 2003

Journal: Interfaces Free Bound.
Volume: 5
Pages: 331-356
Year: 2003


We rigorously derive the notion of crystalline mean curvature af an anisotropic partition with no restriction on the space dimension. Our results cover the case of crystalline networks in two dimensions, polyhedral partitions in three dimensions, and generic anisotropic partitions for smooth anisotropies. The natural equilibrium conditions on the singular set of the partition are derived. We discuss several examples in two dimensions (also for two adjacent triple junctions) and one example in three dimensions when the Wulff shape is the unit cube. In the examples we analyze also the stability of the partitions.

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