# A diffused interface whose chemical potential lies in a Sobolev space

Yoshihiro Tonegawa^{[1]}

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

- Volume: 4, Issue: 3, page 487-510
- ISSN: 0391-173X

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topTonegawa, Yoshihiro. "A diffused interface whose chemical potential lies in a Sobolev space." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.3 (2005): 487-510. <http://eudml.org/doc/84568>.

@article{Tonegawa2005,

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 $\varepsilon $ tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.},

affiliation = {Department of Mathematics Hokkaido University Sapporo 060-0810, Japan},

author = {Tonegawa, Yoshihiro},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

language = {eng},

number = {3},

pages = {487-510},

publisher = {Scuola Normale Superiore, Pisa},

title = {A diffused interface whose chemical potential lies in a Sobolev space},

url = {http://eudml.org/doc/84568},

volume = {4},

year = {2005},

}

TY - JOUR

AU - Tonegawa, Yoshihiro

TI - A diffused interface whose chemical potential lies in a Sobolev space

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2005

PB - Scuola Normale Superiore, Pisa

VL - 4

IS - 3

SP - 487

EP - 510

AB - 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 $\varepsilon $ tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.

LA - eng

UR - http://eudml.org/doc/84568

ER -

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