[Extension de la formule de Reilly avec applications aux estimées de valeurs propres pour les laplaciens avec dérive]
Dans cette Note, nous étendons la formule de Reilly au cas des opérateurs Laplaciens avec dérive, et l'appliquons à l'étude d'estimées de valeurs propres pour de tels opérateurs sur des variétés riemanniennes compactes à bord. Nos estimées généralisent des résultats antérieurs de Reilly ainsi que de Choi et Wang.
In this Note, we extend the Reilly formula for drifting Laplacian operator and apply it to study eigenvalue estimate for drifting Laplacian operators on compact Riemannian manifolds' boundary. Our results on eigenvalue estimates extend previous results of Reilly and Choi and Wang.
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@article{CRMATH_2010__348_21-22_1203_0,
author = {Ma, Li and Du, Sheng-Hua},
title = {Extension of {Reilly} formula with applications to eigenvalue estimates for drifting {Laplacians}},
journal = {Comptes Rendus. Math\'ematique},
pages = {1203--1206},
publisher = {Elsevier},
volume = {348},
number = {21-22},
year = {2010},
doi = {10.1016/j.crma.2010.10.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.10.003/}
}
TY - JOUR AU - Ma, Li AU - Du, Sheng-Hua TI - Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians JO - Comptes Rendus. Mathématique PY - 2010 SP - 1203 EP - 1206 VL - 348 IS - 21-22 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.10.003/ DO - 10.1016/j.crma.2010.10.003 LA - en ID - CRMATH_2010__348_21-22_1203_0 ER -
%0 Journal Article %A Ma, Li %A Du, Sheng-Hua %T Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians %J Comptes Rendus. Mathématique %D 2010 %P 1203-1206 %V 348 %N 21-22 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.10.003/ %R 10.1016/j.crma.2010.10.003 %G en %F CRMATH_2010__348_21-22_1203_0
Ma, Li; Du, Sheng-Hua. Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians. Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1203-1206. doi : 10.1016/j.crma.2010.10.003. http://www.numdam.org/articles/10.1016/j.crma.2010.10.003/
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☆ The research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20090002110019.
