Convergence of perturbed Allen-Cahn equations to forced mean curvature flow Luca MugnaiMatthias Roeger 53C4435K5549Q15Allen-Cahn equationsharp interface limitsmotion by mean curvature 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. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.3949 10.1512/iumj.2011.60.3949 en Indiana Univ. Math. J. 60 (2011) 41 - 76 state-of-the-art mathematics http://iumj.org/access/