[Un problème ouvert sur les Jacobiens soulevé par Bourgain, Brezis et Mironescu]
Nous démontrons une estimée pour des Jacobiens dans le contexte de la fonctionnelle de Ginzburg–Landau. Cela répond à une conjecture dans un travail récent de Bourgain, Brezis et Mironescu.
We establish a Jacobian estimate in the context of Ginzburg–Landau theory, which was conjectured in a recent work of Bourgain, Brezis and Mironescu.
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@article{CRMATH_2003__337_6_381_0,
author = {Bethuel, Fabrice and Orlandi, Giandomenico and Smets, Didier},
title = {On an open problem for {Jacobians} raised by {Bourgain,} {Brezis} and {Mironescu}},
journal = {Comptes Rendus. Math\'ematique},
pages = {381--385},
publisher = {Elsevier},
volume = {337},
number = {6},
year = {2003},
doi = {10.1016/S1631-073X(03)00367-4},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00367-4/}
}
TY - JOUR AU - Bethuel, Fabrice AU - Orlandi, Giandomenico AU - Smets, Didier TI - On an open problem for Jacobians raised by Bourgain, Brezis and Mironescu JO - Comptes Rendus. Mathématique PY - 2003 SP - 381 EP - 385 VL - 337 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00367-4/ DO - 10.1016/S1631-073X(03)00367-4 LA - en ID - CRMATH_2003__337_6_381_0 ER -
%0 Journal Article %A Bethuel, Fabrice %A Orlandi, Giandomenico %A Smets, Didier %T On an open problem for Jacobians raised by Bourgain, Brezis and Mironescu %J Comptes Rendus. Mathématique %D 2003 %P 381-385 %V 337 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00367-4/ %R 10.1016/S1631-073X(03)00367-4 %G en %F CRMATH_2003__337_6_381_0
Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier. On an open problem for Jacobians raised by Bourgain, Brezis and Mironescu. Comptes Rendus. Mathématique, Tome 337 (2003) no. 6, pp. 381-385. doi : 10.1016/S1631-073X(03)00367-4. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00367-4/
[1] G. Alberti, S. Baldo, G. Orlandi, Variational convergence for functionals of Ginzburg–Landau type, Preprint, 2002
[2] J. Bourgain, H. Brezis, Work on the curl–div system, in preparation
[3] J. Bourgain, H. Brezis, P. Mironescu, H1/2 maps with values into the circle: minimal connections, lifting, and the Ginzburg–Landau equation, in press
[4] F. Bethuel, G. Orlandi, D. Smets, Approximation with bounded vorticity for the Ginzburg–Landau functional, in preparation
[5] Ginzburg–Landau Vortices, Birkhäuser, Boston, 1994
[6] Geometric Measure Theory, Springer, Berlin, 1969
[7] Lower bounds for generalized Ginzburg–Landau functionals, SIAM J. Math. Anal., Volume 30 (1999), pp. 721-746
[8] The Jacobian and the Ginzburg–Landau energy, Calc. Var. Partial Differential Equations, Volume 14 (2002), pp. 151-191
[9] Lower bounds for the energy of unit vector fields and applications, J. Funct. Anal., Volume 152 (1998), pp. 379-403
[10] A rigorous derivation of a free-boundary problem arising in superconductivity, Ann. Sci. ENS, Volume 33 (2000), pp. 561-592
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