no. 7
Strong diamagnetism for general domains and application
Fournais, Soeren1; Helffer, Bernard2
1 Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France) and University of Aarhus Department of Mathematical Sciences Ny Munkegade, Building 1530 8000 Aarhus C (Denmark)
2 Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France)
Annales de l'Institut Fourier, Volume 57 (2007) no. 7, pp. 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: 10.5802/aif.2337
Classification: 35P15, 35J55, 82D55
Keywords: Spectral theory, bottom of the spectrum, Neumann condition, superconductivity
Mot clés : théorie spectrale, bas du spectre, condition de Neumann, supraconductivité

Fournais, Soeren 1; Helffer, Bernard 2

1 Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France) and University of Aarhus Department of Mathematical Sciences Ny Munkegade, Building 1530 8000 Aarhus C (Denmark)
2 Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France) 
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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/articles/10.5802/aif.2337/

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