JournalsifbVol. 8 , No. 3DOI 10.4171/ifb/146

On a uniform approximation of motion by anisotropic curvature by the Allen–Cahn equations

  • Yoshikazu Giga

    University of Tokyo, Japan
  • Reiner Schätzle

    Universität Tübingen, Germany
  • Takeshi Ohtsuka

    University of Tokyo, Japan
On a uniform approximation of motion by anisotropic curvature by the Allen–Cahn equations cover

Abstract

The convergence of solutions of anisotropic Allen–Cahn equations is studied when the interface thickness parameter (denoted by ε) tends to zero. It is shown that the convergence to a level set solution of the corresponding anisotropic interface equations is uniform with respect to the derivatives of a surface energy density function. As an application the crystalline motion of interfaces is shown to be approximated by the anisotropic Allen–Cahn equations.