The Li-Yau semiclassical lower bound for the sum of the first 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 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}, 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}, zbl = {0957.35104}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1777/} }
TY - JOUR AU - Erdös, László AU - Loss, Michael AU - Vougalter, Vitali TI - Diamagnetic behavior of sums Dirichlet eigenvalues JO - Annales de l'Institut Fourier PY - 2000 SP - 891 EP - 907 VL - 50 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1777/ DO - 10.5802/aif.1777 LA - en ID - AIF_2000__50_3_891_0 ER -
%0 Journal Article %A Erdös, László %A Loss, Michael %A Vougalter, Vitali %T Diamagnetic behavior of sums Dirichlet eigenvalues %J Annales de l'Institut Fourier %D 2000 %P 891-907 %V 50 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1777/ %R 10.5802/aif.1777 %G en %F 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://archive.numdam.org/articles/10.5802/aif.1777/
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