Diffused interface with the chemical potential in the Sobolev spacePreprint Series # 714
AbstractWe study a singular perturbation problem arising in the scalar twophase 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 $\e$ tending to zero is an integral varifold with the sharp integrability condition on the mean curvature
