Optimal Interface Error Estimates for the Mean Curvature Flow

摘要

We study a double obstacle problem for a singularly perturbed reaction diffusionequation with a small parameter epsilon > 0. This problem is viewed as an approximation for the classical mean curvature flow. We derive an optimal error estimate of order O(epsilon(sup 2)) for the interfaces, which is valid before the onset of singularities. The proof is based on constructing suitable sub and supersolutions.