Unstable crystalline Wulff shapes in 3D

Maurizio Paolini, Franco Pasquarelli

Risultato della ricerca: Contributo in libroContributo a convegno


We investigate the stability of the evolution by anysotropic and crystalline curvature starting from an initial surface equal to the Wulff shape. It is well known that the Wulff shape evolves selfsimilarly according to the law $V=-\kappa_\phi n_\phi$. Here the index $\phi$ refers to the underlying anisotropy described by the Wulff shape, so that $\kappa_\phi$ is the relative mean curvature and $n_\phi$ is the Cahn-Hoffmann conormal vector field. Such selfsimilar evolution is also known to be stable under small perturbations of the initial surface in the isotropic setting (the Wulff shape is a sphere) or in 2D if the underlying anisotropy is symmetric. We show that this evolution is unstable for some specific choices of the Wulff shape both rotationally symmetric and fully crystalline.
Lingua originaleEnglish
Titolo della pubblicazione ospiteProgress in Nonlinear Differential Equations and Their Applications 51
Numero di pagine13
Stato di pubblicazionePubblicato - 2002
EventoVariational methods for discontinuous structures - Cernobbio
Durata: 4 lug 20016 lug 2001


ConvegnoVariational methods for discontinuous structures


  • crystalline anisotropy
  • selfsimilar evolution
  • wulff shape


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