We show two examples of facet-breaking for three-dimensional polyhedral surfaces evolving by crystalline mean curvature. The analysis shows that creation of new facets during the evolution is a common phenomenon. The first example is completely rigorous, and the evolution after the subdivision of one facet is explicitly computed for short times. Moreover, the constructed evolution is unique among the crystalline flows with the given initial datum. The second example suggests that curved portions of the boundary may appear even starting from a polyhedral set close to the Wulff shape.

Bellettini, G., Novaga, M., Paolini, M., Facet-breaking for three dimensional crystals evolving by mean curvature, <<INTERFACES AND FREE BOUNDARIES>>, 1999; 1 (1): 39-55. [doi:10.4171/IFB/3] [http://hdl.handle.net/10807/20938]

Facet-breaking for three dimensional crystals evolving by mean curvature

Bellettini, Giovanni;Novaga, Matteo;Paolini, Maurizio
1999

Abstract

We show two examples of facet-breaking for three-dimensional polyhedral surfaces evolving by crystalline mean curvature. The analysis shows that creation of new facets during the evolution is a common phenomenon. The first example is completely rigorous, and the evolution after the subdivision of one facet is explicitly computed for short times. Moreover, the constructed evolution is unique among the crystalline flows with the given initial datum. The second example suggests that curved portions of the boundary may appear even starting from a polyhedral set close to the Wulff shape.
1999
Inglese
Bellettini, G., Novaga, M., Paolini, M., Facet-breaking for three dimensional crystals evolving by mean curvature, <<INTERFACES AND FREE BOUNDARIES>>, 1999; 1 (1): 39-55. [doi:10.4171/IFB/3] [http://hdl.handle.net/10807/20938]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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: https://hdl.handle.net/10807/20938
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 44
  • ???jsp.display-item.citation.isi??? ND
social impact