We rigorously derive the notion of crystalline mean curvature of 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 also analyze the stability of the partitions.

Bellettini, G., Novaga, M., & Riey, G. (2003). First variation of anisotropic energies and crystalline mean curvature for partitions. INTERFACES AND FREE BOUNDARIES, 5(3), 331-356.

First variation of anisotropic energies and crystalline mean curvature for partitions

BELLETTINI, GIOVANNI;
2003

Abstract

We rigorously derive the notion of crystalline mean curvature of 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 also analyze the stability of the partitions.
Bellettini, G., Novaga, M., & Riey, G. (2003). First variation of anisotropic energies and crystalline mean curvature for partitions. INTERFACES AND FREE BOUNDARIES, 5(3), 331-356.
File in questo prodotto:
File Dimensione Formato  
2003_Bellettini_Novaga_Riey_Interfaces_Free_Bound.pdf

non disponibili

Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 274.93 kB
Formato Adobe PDF
274.93 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/1017438