A diffused interface whose chemical potential lies in a Sobolev space

Tonegawa, Yoshihiro

Geodesic

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A diffused interface whose chemical potential lies in a Sobolev space

Tonegawa, Yoshihiro ¹

¹ Department of Mathematics Hokkaido University Sapporo 060-0810, Japan

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 487-510

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Résumé

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 $ε$ tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.

MR Zbl

Classification : 35J60, 35B25, 35J20, 80A22

Affiliations des auteurs :

Tonegawa, Yoshihiro ¹

¹ Department of Mathematics Hokkaido University Sapporo 060-0810, Japan

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     title = {A diffused interface whose chemical potential lies in a {Sobolev} space},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {487--510},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {3},
     year = {2005},
     mrnumber = {2185866},
     zbl = {1170.35416},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_3_487_0/}
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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, Série 5, Tome 4 (2005) no. 3, pp. 487-510. http://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_3_487_0/