# Diffused interface with the chemical potential in the Sobolev space

Preprint Series # 714
Tonegawa, Yoshihiro Diffused interface with the chemical potential in the Sobolev space. (2005);

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## 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 $\e$ tending to zero is an integral varifold with the sharp integrability condition on the mean curvature

Item Type: Preprint 00-xx GENERAL 915