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

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.

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.

@article{AIF_2000__50_3_891_0,
     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {3},
     year = {2000},
     pages = {891-907},
     doi = {10.5802/aif.1777},
     zbl = {0957.35104},
     mrnumber = {2001g:35201},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2000__50_3_891_0}
}
Erdös, László; Loss, Michael; Vougalter, Vitali. Diamagnetic behavior of sums Dirichlet eigenvalues. Annales de l'Institut Fourier, Volume 50 (2000) no. 3, pp. 891-907. doi : 10.5802/aif.1777. http://www.numdam.org/item/AIF_2000__50_3_891_0/

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