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

Preprint Series # 738
Giga, Yoshikazu and Ohtsuka, Takeshi and Schaetzle, Reiner On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations. (2005);

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## Abstract

The convergence of solutions of anisotropic Allen-Cahn equations is studied when the interface thickness parameter(denoted by $\varepsilon$) 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 suface energy density function. As an application a cryatalline motion of interfaces in shown to be approximated by anisotropic Allen-Cahn equations.

Item Type: Preprint anisotropic Allen-Cahn equation, anisotropic mean curvature flow, viscosity solution, crystalline curvature flow 53-xx DIFFERENTIAL GEOMETRY35-xx PARTIAL DIFFERENTIAL EQUATIONS 1034