TY - JOUR
T1 - Compactness in Ginzburg-Landau energy by kynetic averaging
AU - Jabin, Pierre Emmanuel
AU - Perthame, Benoît
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2000/9/15
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
M3 - Article
AN - SCOPUS:17044461603
SN - 0764-4442
VL - 331
SP - 441
EP - 445
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 -