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A diffused interface whose chemical potential lies in a Sobolev space

Yoshihiro Tonegawa — 2005

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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 > n 2 and n is the dimension of the domain. We show that the limit interface as ε tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.

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