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