Compacité par lemmes de moyenne cinétiques pour des énergies de Ginzburh-Landau

Pierre Emmanuel Jabin; Benoît Perthame

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

Compacité par lemmes de moyenne cinétiques pour des énergies de Ginzburh-Landau

Translated title of the contribution: 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.

Translated title of the contribution	Compactness in Ginzburg-Landau energy by kynetic averaging
Original language	French
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

Mathematics(all)

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10.1016/s0764-4442(00)01622-0

Cite this

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title = "Compacit{\'e} par lemmes de moyenne cin{\'e}tiques pour des {\'e}nergies de Ginzburh-Landau",

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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year = "2000",

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

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

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ER -

Compacité par lemmes de moyenne cinétiques pour des énergies de Ginzburh-Landau

Abstract

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