%0 Journal Article
%T Convergence of perturbed Allen-Cahn equations to forced mean curvature flow
%A Luca Mugnai
%A Matthias R£żger
%J Mathematics
%D 2009
%I arXiv
%X We study perturbations of the Allen-Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and apply previous results for the Allen-Cahn action functional. Finally we discuss some applications.
%U http://arxiv.org/abs/0902.1816v1