Magnetic bottles for the Neumann problem : curvature effects in the case of dimension $3$ (general case)

Helffer, Bernard; Morame, Abderemane

doi:10.1016/j.ansens.2003.04.003

Magnetic bottles for the Neumann problem : curvature effects in the case of dimension

3

(general case)

Helffer, Bernard ; Morame, Abderemane

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 1, pp. 105-170.

MR Zbl | 3 citations dans Numdam

DOI : 10.1016/j.ansens.2003.04.003

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     author = {Helffer, Bernard and Morame, Abderemane},
     title = {Magnetic bottles for the {Neumann} problem : curvature effects in the case of dimension $3$ (general case)},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {105--170},
     publisher = {Elsevier},
     volume = {Ser. 4, 37},
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     year = {2004},
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Helffer, Bernard; Morame, Abderemane. Magnetic bottles for the Neumann problem : curvature effects in the case of dimension $3$ (general case). Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 1, pp. 105-170. doi : 10.1016/j.ansens.2003.04.003. http://archive.numdam.org/articles/10.1016/j.ansens.2003.04.003/

Bibliographie
Cité par

[1] Agmon S., Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations, Math. Notes, vol. 29, Princeton University Press, 1982. | MR | Zbl

[2] Bauman P., Phillips D., Tang Q., Stable nucleation for the Ginzburg-Landau system with an applied magnetic field, IMA Preprint Series 1416 (1996) , Arch. Rational Mech. Anal. 142 (1998) 1-43. | MR | Zbl

[3] Bernoff A., Sternberg P., Onset of superconductivity in decreasing fields for general domains, J. Math. Phys. 39 (1998) 1272-1284. | MR | Zbl

[4] Bolley C., Modélisation du champ de retard à la condensation d'un supraconducteur par un problème de bifurcation, M 26 (2) (1992) 235-287. | Numdam | MR | Zbl

[5] E.B. Davies, Spectral Theory and Differential Operators, in: Cambridge Studies in Advanced Mathematics. | Zbl

[6] Dauge M., Helffer B., Eigenvalues variation I, Neumann problem for Sturm-Liouville operators, J. Differential Equations 104 (2) (1993) 243-262. | MR | Zbl

[7] Dierkes U., Hildebrandt S., Kuster A., Wohlrab O., Minimal Surfaces I, Springer-Verlag, Berlin, 1992. | MR | Zbl

[8] Helffer B., Introduction to the Semiclassical Analysis for the Schrödinger Operator and Applications, Springer Lecture Notes in Math., vol. 1336, 1988. | MR | Zbl

[9] Helffer B., Semi-classical analysis for the Schrödinger operator with magnetic wells (after R. Montgomery, B. Helffer and A. Mohamed), in: Proceedings of the Conference in Minneapolis, IMA Volumes in Mathematics and its Applications, vol. 95, Springer-Verlag, 1997, pp. 99-114. | MR | Zbl

[10] Helffer B., Bouteilles magnétiques et supraconductivité (d'après Helffer-Morame, Lu-Pan et Helffer-Pan), Séminaire EDP de l'École Polytechnique 2000-2001, Reprint , http://www.math.polytechnique.fr. | Numdam | MR | Zbl

[11] Helffer B., Mohamed A., Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells, J. Funct. Anal. 138 (1) (1996) 40-81. | MR | Zbl

[12] Helffer B., Morame A., Magnetic bottles in connection with superconductivity, J. Funct. Anal. 185 (2) (2001) 604-680. | MR | Zbl

[13] Helffer B., Morame A., Magnetic bottles in connection with superconductivity: Case of dimension 3, Proc. Indian Acad. Sci. (Math. Sci.) 112 (1) (2002). | MR

[14] B. Helffer, A. Morame, Magnetic bottles for the Neumann problem: Curvature effects in the case of dimension 3, Preprint mp_arc 01-362, 2001. | MR

[15] B. Helffer, A. Morame, Magnetic bottles for the Neumann problem: Curvature effects in the case of dimension 3, general case, Preprint mp_arc 02-145, 2002.

[16] Helffer B., Nourrigat J., Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progress in Mathematics, vol. 58, Birkhäuser, 1985. | MR | Zbl

[17] Helffer B., Pan X.-B., Upper critical field and location of surface nucleation of superconductivity, Annales de l'Institut Henri Poincaré (Analyse Non Linéaire) 20 (1) (2003) 145-181. | Numdam | MR | Zbl

[18] Helffer B., Sjöstrand J., Multiple wells in the semiclassical limit I, Comm. PDE 9 (4) (1984) 337-408. | MR | Zbl

[19] Lu K., Pan X.-B., Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Phys. D 127 (1999) 73-104. | MR | Zbl

[20] Lu K., Pan X.-B., Eigenvalue problems of Ginzburg-Landau operator in bounded domains, J. Math. Phys. 40 (6) (1999) 2647-2670. | MR | Zbl

[21] Lu K., Pan X.-B., Gauge invariant eigenvalue problems on R² and R²₊, Trans. Amer. Math. Soc. 352 (3) (2000) 1247-1276. | MR | Zbl

[22] Lu K., Pan X.-B., Ginzburg-Landau system and surface nucleation of superconductivity, in: Proceeding of the IMS Workshop on Reaction-Diffusion systems, Chinese University of Hong-Kong, 1999.

[23] Lu K., Pan X.-B., Surface nucleation of superconductivity in 3-dimension, J. Differential Equations 168 (2) (2000) 386-452. | MR | Zbl

[24] Montgomery R., Hearing the zerolocus of a magnetic field, Comm. Math. Phys. 168 (1995) 651-675. | MR | Zbl

[25] Pan X.-B., Upper critical field for superconductors with edges and corners, Calc. Var. PDE 14 (2002) 447-482. | MR | Zbl

[26] X.-B. Pan, Surface conductivity in 3 dimensions, Personal communication, October 2001, Unpublished.

[27] Pan X.-B., Kwek K.-H., Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domain, Trans. Amer. Math. Soc. 354 (10) (2002) 4201-4227. | MR | Zbl

[28] Del Pino M., Felmer P.L., Sternberg P., Boundary concentration for eigenvalue problems related to the onset of superconductivity, Comm. Math. Phys. 210 (2000) 413-446. | MR | Zbl

[29] Reed M., Simon B., Methods of modern Mathematical Physics, IV: Analysis of Operators, Academic Press, New York, 1978. | MR | Zbl

[30] Saint-James D., Sarma G., Thomas E.J., Type II Superconductivity, Pergamon, Oxford, 1969.

[31] Spivak M., Differential Geometry, Publish or Perish, Houston, 1975.

[32] Thaller B., The Dirac Equation, Texts and Monographs in Physics, Springer-Verlag, 1992. | MR | Zbl

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