Line-energy Ginzburg-Landau models : zero-energy states

Pierre-Emmanuel Jabin; Felix Otto; BenoÎt Perthame

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 1, page 187-202
  • ISSN: 0391-173X

Abstract

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We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful analysis of the corresponding weak solutions by the method of characteristics.

How to cite

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Jabin, Pierre-Emmanuel, Otto, Felix, and Perthame, BenoÎt. "Line-energy Ginzburg-Landau models : zero-energy states." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.1 (2002): 187-202. <http://eudml.org/doc/84463>.

@article{Jabin2002,
abstract = {We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful analysis of the corresponding weak solutions by the method of characteristics.},
author = {Jabin, Pierre-Emmanuel, Otto, Felix, Perthame, BenoÎt},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {187-202},
publisher = {Scuola normale superiore},
title = {Line-energy Ginzburg-Landau models : zero-energy states},
url = {http://eudml.org/doc/84463},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Jabin, Pierre-Emmanuel
AU - Otto, Felix
AU - Perthame, BenoÎt
TI - Line-energy Ginzburg-Landau models : zero-energy states
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 1
SP - 187
EP - 202
AB - We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful analysis of the corresponding weak solutions by the method of characteristics.
LA - eng
UR - http://eudml.org/doc/84463
ER -

References

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  9. [9] P. E. Jabin – B. Perthame, Compactness in Ginzburg-Landau energy by kinetic averaging, Comm. Pure Appl. Math. 54 (2001), 1096-1109. Zbl1124.35312MR1835383
  10. [10] W. Jin – R. V. Kohn, Singular perturbation and the energy of folds, J. Nonlinear Sci 10 (2000), 355-390. Zbl0973.49009MR1752602
  11. [11] T. Rivière – S. Serfaty, Limiting domain wall energy in micromagnetism, Comm. Pure Appl. Math. 54 (2001), 294-338. Zbl1031.35142MR1809740
  12. [12] T. Rivière – S. Serfaty, Compactness, kinetic formulation, and entropies for a problem related to micromagnetics, preprint (2001). Zbl1094.35125MR1974456
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Citations in EuDML Documents

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  1. Andrew Lorent, A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
  2. Andrew Lorent, A simple proof of the characterization of functions of low Aviles Giga energy on a ball regularity
  3. Pierre-Emmanuel Jabin, Benoît Perthame, Kinetic methods for Line-energy Ginzburg–Landau models
  4. Pierre-Emmanuel Jabin, Benoît Perthame, Regularity in kinetic formulations via averaging lemmas
  5. Pierre-Emmanuel Jabin, Benoît Perthame, Regularity in kinetic formulations via averaging lemmas

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