no. 3
Diamagnetic behavior of sums Dirichlet eigenvalues
Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 891-907.

Nous étendons la borne inférieure semi-classique due à Li-Yau pour la somme des N premières valeurs propres du laplacien de Dirichlet aux laplaciens de Dirichlet avec un champ magnétique constant. Notre méthode repose sur une nouvelle inégalité pour les champs magnétiques constants.

The Li-Yau semiclassical lower bound for the sum of the first N eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.

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     author = {Erd\"os, L\'aszl\'o and Loss, Michael and Vougalter, Vitali},
     title = {Diamagnetic behavior of sums {Dirichlet} eigenvalues},
     journal = {Annales de l'Institut Fourier},
     pages = {891--907},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {3},
     year = {2000},
     doi = {10.5802/aif.1777},
     mrnumber = {2001g:35201},
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     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1777/}
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Erdös, László; Loss, Michael; Vougalter, Vitali. Diamagnetic behavior of sums Dirichlet eigenvalues. Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 891-907. doi : 10.5802/aif.1777. http://www.numdam.org/articles/10.5802/aif.1777/

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