Strong diamagnetism for general domains and application
Annales de l'Institut Fourier, Volume 57 (2007) no. 7, p. 2389-2400
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.
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.
DOI : https://doi.org/10.5802/aif.2337
Classification:  35P15,  35J55,  82D55
Keywords: Spectral theory, bottom of the spectrum, Neumann condition, superconductivity 
@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 = {https://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, Volume 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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