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, p. 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 $p>\frac{n}{2}$ and $n$ is the dimension of the domain. We show that the limit interface as $\epsilon$ tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.

Classification:  35J60,  35B25,  35J20,  80A22
@article{ASNSP_2005_5_4_3_487_0,
author = {Tonegawa, Yoshihiro},
title = {A diffused interface whose chemical potential lies in a Sobolev space},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {3},
year = {2005},
pages = {487-510},
zbl = {1170.35416},
mrnumber = {2185866},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2005_5_4_3_487_0}
}

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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