Geodesic
First variation of anisotropic energies and crystalline mean curvature of partitions
Giovanni Bellettini1 ; Giuseppe Riey2 ; Matteo Novaga3 orcid
1Università di Roma 'Tor Vergata', Italy
2Università di Roma, Italy
3Università di Pisa, Italy
Interfaces and free boundaries, Tome 5 (2003) no. 3, pp. 331-356

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DOI

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.
DOI : 10.4171/ifb/82
Classification : 35-XX, 65-XX, 74-XX, 00-XX
Mots-clés : crystalline mean curvature; anisotropic energy

Giovanni Bellettini  1   ; Giuseppe Riey  2   ; Matteo Novaga  3

1 Università di Roma 'Tor Vergata', Italy
2 Università di Roma, Italy
3 Università di Pisa, Italy 
Giovanni Bellettini; Giuseppe Riey; Matteo Novaga. First variation of anisotropic energies and crystalline mean curvature of partitions. Interfaces and free boundaries, Tome 5 (2003) no. 3, pp. 331-356. doi: 10.4171/ifb/82
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