[Une inégalité isopérimétrique pour la valeur propre principale du laplacien avec transport]
Nous généralisons l'inégalité classique de Rayleigh–Faber–Krahn au cas du laplacien Dirichlet avec un terme de transport. Nous résolvons également des problèmes d'optimisation pour la valeur propre principale de l'opérateur dans un domaine fixé et avec un contrôle sur le terme de transport v.
We generalize the classical Rayleigh–Faber–Krahn inequality to the case of the Dirichlet Laplacian with a drift. We also solve some optimization problems for the principal eigenvalue of the operator in a fixed domain with a control of the drift v in .
Publié le :
@article{CRMATH_2005__340_5_347_0,
author = {Hamel, Fran\c{c}ois and Nadirashvili, Nikolai and Russ, Emmanuel},
title = {An isoperimetric inequality for the principal eigenvalue of the {Laplacian} with drift},
journal = {Comptes Rendus. Math\'ematique},
pages = {347--352},
publisher = {Elsevier},
volume = {340},
number = {5},
year = {2005},
doi = {10.1016/j.crma.2005.01.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.01.012/}
}
TY - JOUR AU - Hamel, François AU - Nadirashvili, Nikolai AU - Russ, Emmanuel TI - An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift JO - Comptes Rendus. Mathématique PY - 2005 SP - 347 EP - 352 VL - 340 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.01.012/ DO - 10.1016/j.crma.2005.01.012 LA - en ID - CRMATH_2005__340_5_347_0 ER -
%0 Journal Article %A Hamel, François %A Nadirashvili, Nikolai %A Russ, Emmanuel %T An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift %J Comptes Rendus. Mathématique %D 2005 %P 347-352 %V 340 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.01.012/ %R 10.1016/j.crma.2005.01.012 %G en %F CRMATH_2005__340_5_347_0
Hamel, François; Nadirashvili, Nikolai; Russ, Emmanuel. An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift. Comptes Rendus. Mathématique, Tome 340 (2005) no. 5, pp. 347-352. doi : 10.1016/j.crma.2005.01.012. http://www.numdam.org/articles/10.1016/j.crma.2005.01.012/
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