Abstract

We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms $W^{1,p}$ of the associated chemical potential fields are bounded uniformly, where $p>\frac{n}{2}$ and $n$ is the dimension of the domain. We show that the limit interface as $\varepsilon $ tends to zero is an integral varifold with a sharp integrability condition on the mean curvature