no. 7
Strong diamagnetism for general domains and application  [ Diamagnétisme fort pour des domaines généraux et applications ]
Annales de l'Institut Fourier, Tome 57 (2007) no. 7, pp. 2389-2400.

Nous considérons le Laplacien de Neumann avec champ magnétique constant dans un domaine régulier de ℝ 2 . Si B désigne l’intensité de ce champ et si λ 1 (B) désigne la première valeur propre de ce Laplacien, il est démontré que λ 1 est une fonction monotone croissante de B pour B grand. En combinant avec des résultats antérieurs des auteurs, ceci implique la coïncidence de toutes les définitions raisonables du troisième champ critique pour les matériaux supraconducteurs de type II.

We consider the Neumann Laplacian with constant magnetic field on a regular domain in ℝ 2 . Let B be the strength of the magnetic field and let λ 1 (B) be the first eigenvalue of this Laplacian. It is proved that B↦λ 1 (B) is monotone increasing for large B. Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.

Reçu le : 2006-08-23
Accepté le : 2007-02-07
DOI : https://doi.org/10.5802/aif.2337
Classification : 35P15,  35J55,  82D55
Mots clés: théorie spectrale, bas du spectre, condition de Neumann, supraconductivité 
@article{AIF_2007__57_7_2389_0,
     author = {Fournais, Soeren and Helffer, Bernard},
     title = {Strong diamagnetism for general domains and application},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {7},
     year = {2007},
     pages = {2389-2400},
     doi = {10.5802/aif.2337},
     zbl = {1133.35073},
     mrnumber = {2394546},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2007__57_7_2389_0/}
}
Fournais, Soeren; Helffer, Bernard. Strong diamagnetism for general domains and application. Annales de l'Institut Fourier, Tome 57 (2007) no. 7, pp. 2389-2400. doi : 10.5802/aif.2337. https://aif.centre-mersenne.org/item/AIF_2007__57_7_2389_0/

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