J. R. Abo-shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Chapitre 5 Stabilization in finite time for a system of damped oscillators Bibliographie, Observation of vortex lattices in Bose-Einstein condensates, pp.476-479, 2001.

A. Aftalion, S. Alama, and L. Bronsard, Giant Vortex and the Breakdown of Strong Pinning in a Rotating Bose-Einstein Condensate, Archive for Rational Mechanics and Analysis, vol.6, issue.2
DOI : 10.1007/s00205-005-0373-6

A. Aftalion and I. Danaila, Giant vortices in combined harmonic and quartic traps, Physical Review A, vol.69, issue.3, 2004.
DOI : 10.1103/PhysRevA.69.033608

URL : https://hal.archives-ouvertes.fr/hal-00008635

A. Aftalion and Q. Du, Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime, Physical Review A, vol.64, issue.6, 2001.
DOI : 10.1103/PhysRevA.64.063603

A. Aftalion and R. L. Jerrard, Shape of vortices for a rotating Bose-Einstein condensate, Physical Review A, vol.66, issue.2, 2002.
DOI : 10.1103/PhysRevA.66.023611

A. Aftalion and T. Rivière, Vortex energy and vortex bending for a rotating Bose-Einstein condensate, Physical Review A, vol.64, issue.4, 2001.
DOI : 10.1103/PhysRevA.64.043611

URL : https://hal.archives-ouvertes.fr/hal-00008644

L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equations, Journal de Math??matiques Pures et Appliqu??es, vol.77, issue.1, pp.1-49, 1998.
DOI : 10.1016/S0021-7824(98)80064-0

F. Almgren, W. Browder, and E. H. Lieb, Co-area, liquid crystals and minimal surfaces, Partial differential equations, Lecture Notes in Math, pp.1-22, 1306.
DOI : 10.1007/978-3-642-55925-9_51

H. Amann and J. I. Díaz, A note on the dynamics of an oscillator in presence of a strong friction, Nonlinear Anal, pp.209-216, 2003.

N. André and I. Shafrir, Minimization of a Ginzburg?Landau type functional with nonvanishing Dirichlet boundary condition, Calc, Var. Partial Differential Equations, vol.7, issue.3, pp.191-217, 1998.

N. André and I. Shafrir, Asymptotic behavior of minimizers for the Ginzburg-Landau functional with weight I, Arch. Rational Mech, Anal, vol.142, issue.1, pp.45-73, 1998.

N. André and I. Shafrir, Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part II, Archive for Rational Mechanics and Analysis, vol.142, issue.1, pp.75-98, 1998.
DOI : 10.1007/s002050050084

S. N. Antontsev, J. I. Díaz, and S. Shmarev, Energy methods for free boundary problems, Applications to nonlinear PDEs and Fluid Mechanics, Progress in Nonlinear Differential Equations and Their Applications 48, 2002.

A. Bamberger and H. Cabannes, Mouvements d'une corde vibrante soumise à un frottement solide, C. R. Acad. Sci. Paris Sé. I Math, vol.292, issue.14, pp.699-702, 1981.

A. Beaulieu and R. Hadiji, On a class of Ginzburg-Landau equations with weight, Panamer. Math. J, vol.5, issue.4, pp.1-33, 1995.

F. Bethuel, A characterization of maps in H1(B3, S2) which can be approximated by smooth maps, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.7, issue.4, pp.269-286, 1990.
DOI : 10.1016/S0294-1449(16)30292-X

F. Bethuel, The approximation problem for Sobolev maps between two manifolds, Acta Mathematica, vol.167, issue.0, pp.3-4, 1991.
DOI : 10.1007/BF02392449

F. Bethuel, H. Brezis, and J. M. Coron, Relaxed energies for harmonic maps, Variational methods, Progress in Nonlinear Differential Equations and Their Applications, pp.37-52, 1988.

F. Bethuel, H. Brezis, and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calculus of Variations and Partial Differential Equations, vol.13, issue.2, pp.123-148, 1993.
DOI : 10.1007/BF01191614

F. Bethuel and T. Rivière, Vortices for a variational problem related to superconductivity, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.12, issue.3, pp.243-303, 1995.
DOI : 10.1016/S0294-1449(16)30157-3

F. Bethuel and X. Zheng, Density of smooth functions between two manifolds in Sobolev spaces, Journal of Functional Analysis, vol.80, issue.1, pp.60-75, 1988.
DOI : 10.1016/0022-1236(88)90065-1

J. Bourgain, H. Brezis, and P. Mironescu, H1/2 maps with values into the circle: Minimal Connections, Lifting, and the Ginzburg???Landau equation, Publications math??matiques de l'IH??S, vol.99, issue.1, pp.99-100, 2004.
DOI : 10.1007/s10240-004-0019-5

H. Brezis, Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert. North-Holland Mathematics Studies 5. Notas de matemática (50), 1973.

H. Brezis, Semilinear equations in ? N without condition at infinity, Applied Mathematics & Optimization, vol.7, issue.1, pp.271-282, 1984.
DOI : 10.1007/BF01449045

H. Brezis, Liquid Crystals and Energy Estimates for S2- Valued Maps
DOI : 10.1007/978-1-4613-8743-5_2

H. Brezis, S k -valued maps with singularities, Topics in calculus of variations (Montecatini Terme 1987) Lecture Notes in Math, 1365.

H. Brezis and J. M. Coron, Large solutions for harmonic maps in two dimensions, Communications in Mathematical Physics, vol.11, issue.2, pp.203-215, 1983.
DOI : 10.1007/BF01210846

H. Brezis, J. M. Coron, and E. H. Lieb, Harmonic maps with defects, Communications in Mathematical Physics, vol.5, issue.4, pp.649-705, 1986.
DOI : 10.1007/BF01205490

H. Brezis and A. Friedman, Estimates on the support of solutions of parabolic variational inequalities, Illinois J. Math, vol.20, issue.1, pp.82-97, 1976.

H. Brezis, P. Mironescu, and A. C. Ponce, W 1,1 -Maps with values into S 1 , Geometric Analysis of PDE and Several Complex Variables, Contemporary Mathematics series

H. Brezis and L. Oswald, Remarks on sublinear elliptic equations, Nonlinear Anal, pp.55-64, 1986.
DOI : 10.1016/0362-546x(86)90011-8

G. Buttazzo, L. De-pascale, and I. Fragalà, Topological equivalence of some variational problems involving distances, Discrete Contin, Dynam. Systems, vol.7, issue.2, pp.247-258, 2001.

H. Cabannes, Mouvement d'une corde vibrante soumise à un frottement solide, C. R. Acad. Sci. Paris Sér. A-B, vol.287, issue.8, pp.671-673, 1978.

H. Cabannes, Study of motions of a vibrating string subject to solid friction, Mathematical Methods in the Applied Sciences, vol.14, issue.1, pp.287-300, 1981.
DOI : 10.1002/mma.1670030120

F. Camilli and A. Siconolfi, Hamilton-Jacobi equation with measurable dependence on the state variable, Adv. Differential Equations, vol.8, issue.6, pp.733-768, 2003.

J. M. Carlson and J. S. Langer, Properties of earthquakes generated by fault dynamics, Physical Review Letters, vol.62, issue.22, 1989.
DOI : 10.1103/PhysRevLett.62.2632

Y. Castin and R. Dum, Bose-Einstein condensates with vortices in rotating traps, The European Physical Journal D, vol.7, issue.3, pp.399-412, 1999.
DOI : 10.1007/s100530050584

D. Maso and G. , Introduction to ?-convergence. Progress in Nonlinear Differential Equations and Their Applications 8, 1993.

D. Cecco, G. Palmieri, and G. , LIP manifolds: from metric to finslerian structure, Mathematische Zeitschrift, vol.58, issue.Suppl., pp.223-237, 1995.
DOI : 10.1007/BF02571901

D. Gennes and P. G. , The physics of liquid crystals, 1974.

D. Pino, M. Felmer, and P. , On the basic concentration estimate for the Ginzburg-Landau equation, Differential Integral Equations, vol.11, issue.5, pp.771-779, 1998.

J. I. Díaz, Anulación de soluciones para operadores acretivos en espacios de Banach, Aplicaciones a ciertos problemas parabólicos no lineales, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. LXXIV, pp.865-880, 1980.

J. I. Díaz and A. Liñán, On the asymptotic behavior of solutions of a damped oscillator under a sublinear friction term : from the exceptional to the generic behaviors, Partial Differential Equations, Lecture Notes in Pure and Appl. Math, vol.229, pp.163-170, 2002.

J. I. Díaz and A. Liñán, On the asymptotic behaviour of solutions of a damped oscillator under a sublinear friction term, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat, vol.95, issue.1, pp.155-160, 2001.

J. I. Díaz and V. Millot, Coulomb friction and oscillation : stabilisation in finite time for a system of damped oscillators, CD-Rom Actas XVIII CEDYA/VIII CMA, Tarragona, 2003.

G. Duvaut and J. L. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques, vol.21, 1972.

J. Ericksen and D. Kinderlehrer, Theory and Applications of liquid crystals, The IMA Volumes in Mathematics and its Applications, 1987.
DOI : 10.1007/978-1-4613-8743-5

A. Farina and F. Ginzburg-landau-to-gross-pitaevskii, From Ginzburg-Landau to Gross-Pitaevskii, Monatshefte f???r Mathematik, vol.139, issue.4, pp.265-269, 2003.
DOI : 10.1007/s00605-002-0514-z

M. Giaquinta, G. Modica, and J. Sou?ek, Cartesian Currents in the Calculus of Variations, I. Cartesian currents, 1998.

M. Giaquinta, G. Modica, and J. Sou?ek, Cartesian Currents in the Calculus of Variations, II. Variational integrals, 1998.

D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, second edition, 1983.

M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, vol.152, 1999.

S. Gueron and I. Shafrir, On a Discrete Variational Problem Involving Interacting Particles, SIAM Journal on Applied Mathematics, vol.60, issue.1, pp.1-17, 2000.
DOI : 10.1137/S0036139997315258

A. Haraux, Synopsis, Proc. of the Roy, pp.213-234, 1979.
DOI : 10.1007/BF00280830

A. Haraux, Systèmes dynamiques et applications, Recherches en Mathématiques Appliquées, vol.17, 1991.

P. Hartman, Ordinary differential equations, 1964.

R. Ignat and V. Millot, Vortices in a 2d rotating Bose???Einstein condensate, Comptes Rendus Mathematique, vol.340, issue.8, pp.571-576, 2005.
DOI : 10.1016/j.crma.2005.03.015

R. Ignat and V. Millot, The critical velocity for vortex existence in a two-dimensional rotating Bose???Einstein condensate, Journal of Functional Analysis, vol.233, issue.1
DOI : 10.1016/j.jfa.2005.06.020

R. Ignat and V. Millot, ENERGY EXPANSION AND VORTEX LOCATION FOR A TWO-DIMENSIONAL ROTATING BOSE???EINSTEIN CONDENSATE, Reviews in Mathematical Physics, vol.18, issue.02
DOI : 10.1142/S0129055X06002607

R. L. Jerrard, More about Bose-Einstein condensate, preprint, 2004.

L. Lassoued, Asymptotics for a Ginzburg-Landau model with pinning, Comm. Appl. Nonlinear Anal, vol.4, issue.2, pp.27-58, 1997.

L. Lassoued and P. Mironescu, Ginzburg-landau type energy with discontinuous constraint, Journal d'Analyse Math??matique, vol.26, issue.1, pp.1-26, 1999.
DOI : 10.1007/BF02791255

C. Lefter and V. Radulescu, On the Ginzburg-Landau energy with weight, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.13, issue.2, pp.171-184, 1996.
DOI : 10.1016/S0294-1449(16)30101-9

D. W. Jordan and P. Smith, Nonlinear ordinary differential equations, Oxford Applied Mathematics and Computing Science Series, 1987.

K. Madison, F. Chevy, J. Dalibard, and W. Wohlleben, Vortex Formation in a Stirred Bose-Einstein Condensate, Physical Review Letters, vol.84, issue.5, 2000.
DOI : 10.1103/PhysRevLett.84.806

K. Madison, F. Chevy, J. Dalibard, and W. Wohlleben, Vortices in a stirred Bose-Einstein condensate, Journal of Modern Optics, vol.60, issue.14-15, p.47, 2000.
DOI : 10.1103/PhysRevLett.84.822

V. Millot, Energy with Weight for S 2 -Valued Maps with Prescribed Singularities, to appear in Calc

V. Millot, The relaxed energy for S 2 -valued maps and measurable weights , to appear in Ann, Inst. H. Poincaré Anal. Non Linéaire

E. Sandier, Lower Bounds for the Energy of Unit Vector Fields and Applications, Journal of Functional Analysis, vol.152, issue.2, pp.379-403, 1998.
DOI : 10.1006/jfan.1997.3170

E. Sandier and S. Serfaty, A rigorous derivation of a free-boundary problem arising in superconductivity, Annales Scientifiques de l'????cole Normale Sup????rieure, vol.33, issue.4, pp.561-592, 2000.
DOI : 10.1016/S0012-9593(00)00122-1

E. Sandier and S. Serfaty, Global minimizers for the Ginzburg???Landau functional below the first critical magnetic field, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.17, issue.1, pp.119-145, 2000.
DOI : 10.1016/S0294-1449(99)00106-7

E. Sandier, S. Serfaty, and . Ginzburg-, Ginzburg-Landau minimizers near the first critical field have bounded vorticity, Calculus of Variations and Partial Differential Equations, vol.17, issue.1, pp.17-28, 2003.
DOI : 10.1007/s00526-002-0158-9

K. Schnee and J. Yngvason, Bosons in disc-shape traps : from 3D to 2D, p.preprint, 2004.

S. Serfaty, LOCAL MINIMIZERS FOR THE GINZBURG???LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I, Communications in Contemporary Mathematics, vol.01, issue.02, pp.213-254, 1999.
DOI : 10.1142/S0219199799000109

S. Serfaty, LOCAL MINIMIZERS FOR THE GINZBURG???LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART II, Communications in Contemporary Mathematics, vol.01, issue.03, pp.295-333, 1999.
DOI : 10.1142/S0219199799000134

S. Serfaty, On a model of rotating superfluids, ESAIM: Control, Optimisation and Calculus of Variations, vol.6, pp.201-238, 2001.
DOI : 10.1051/cocv:2001108

M. Struwe, An asymptotic estimate for the Ginzburg-Landau model, C. R. Acad. Sci. Paris Sér. I, vol.317, issue.7, pp.677-680, 1993.

M. Struwe, On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions, Differential and Integral Equations, vol.7, pp.5-6, 1994.

S. Venturini, Derivation of distance functions in, 1991.