A diffused interface whose chemical potential lies in a Sobolev space
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 3, pp. 487-510.

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.

Classification: 35J60, 35B25, 35J20, 80A22
Tonegawa, Yoshihiro 1

1 Department of Mathematics Hokkaido University Sapporo 060-0810, Japan
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Tonegawa, Yoshihiro. A diffused interface whose chemical potential lies in a Sobolev space. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 3, pp. 487-510. http://www.numdam.org/item/ASNSP_2005_5_4_3_487_0/

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