# 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

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topJabin, 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 -

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## Citations in EuDML Documents

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

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