Compactness in Ginzburg-Landau energy by kynetic averaging

Pierre Emmanuel Jabin; Benoît Perthame

doi:10.1016/s0764-4442(00)01622-0

Compactness in Ginzburg-Landau energy by kynetic averaging

Pierre Emmanuel Jabin
, Benoît Perthame

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider a Ginzburg-Landau energy for two-dimensional divergence free fields appearing in the gradient theory of phase transition for instance. We prove that, as the relaxation parameter vanishes, families of such fields with finite energy are compact in L^p (Ω) and we give some information on the limit. Our proof is based on a kinetic interpretation of the entropies which were introduced by Desimone, Kohn, Müller and Otto.

Original language	English (US)
Pages (from-to)	441-445
Number of pages	5
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	331
Issue number	6
DOIs	https://doi.org/10.1016/s0764-4442(00)01622-0
State	Published - Sep 15 2000

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/s0764-4442(00)01622-0

Cite this

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title = "Compactness in Ginzburg-Landau energy by kynetic averaging",

abstract = "We consider a Ginzburg-Landau energy for two-dimensional divergence free fields appearing in the gradient theory of phase transition for instance. We prove that, as the relaxation parameter vanishes, families of such fields with finite energy are compact in Lp (Ω) and we give some information on the limit. Our proof is based on a kinetic interpretation of the entropies which were introduced by Desimone, Kohn, M{\"u}ller and Otto.",

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AU - Jabin, Pierre Emmanuel

AU - Perthame, Benoît

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Y1 - 2000/9/15

N2 - We consider a Ginzburg-Landau energy for two-dimensional divergence free fields appearing in the gradient theory of phase transition for instance. We prove that, as the relaxation parameter vanishes, families of such fields with finite energy are compact in Lp (Ω) and we give some information on the limit. Our proof is based on a kinetic interpretation of the entropies which were introduced by Desimone, Kohn, Müller and Otto.

AB - We consider a Ginzburg-Landau energy for two-dimensional divergence free fields appearing in the gradient theory of phase transition for instance. We prove that, as the relaxation parameter vanishes, families of such fields with finite energy are compact in Lp (Ω) and we give some information on the limit. Our proof is based on a kinetic interpretation of the entropies which were introduced by Desimone, Kohn, Müller and Otto.

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UR - https://www.scopus.com/pages/publications/17044461603#tab=citedBy

U2 - 10.1016/s0764-4442(00)01622-0

DO - 10.1016/s0764-4442(00)01622-0

M3 - Article

AN - SCOPUS:17044461603

SN - 0764-4442

VL - 331

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JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 6

ER -

Compactness in Ginzburg-Landau energy by kynetic averaging

Abstract

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