## Abstract

The evolution equations of crystal growth often employ a regularization of the surface energy based on a corner energy term. Here, we consider the effect of this regularization on the equilibrium shape of a solid particle in three dimensions. We determine that a sufficient regularization involves only one of the two isotropic invariants related to curvature. Using a long-wave approximation, we derive a non-linear equation for the shape of a semi-infinite wedge in the case when the surface energy has cubic symmetry. An analytic description of the solution along an edge is given as well as an exact solution for a special case of anisotropy. Finally, this equation is solved numerically to demonstrate explicit solutions for which the regularization rounds the edges of the unregularized crystal shape.

Original language | English (US) |
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Pages (from-to) | 190-205 |

Number of pages | 16 |

Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |

Volume | 75 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2010 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics