JournalsifbVol. 5, No. 3pp. 331–356

First variation of anisotropic energies and crystalline mean curvature of partitions

  • Giovanni Bellettini

    Università di Roma 'Tor Vergata', Italy
  • Giuseppe Riey

    Università di Roma, Italy
  • Matteo Novaga

    Università di Pisa, Italy
First variation of anisotropic energies and crystalline mean curvature of partitions cover
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Abstract

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.

Cite this article

Giovanni Bellettini, Giuseppe Riey, Matteo Novaga, First variation of anisotropic energies and crystalline mean curvature of partitions. Interfaces Free Bound. 5 (2003), no. 3, pp. 331–356

DOI 10.4171/IFB/82