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

Abstract

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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.

How to cite

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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 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 $p&gt;\frac\{n\}\{2\}$ 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 $p&gt;\frac{n}{2}$ 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 -

References

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