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Estimation of spectral gap for elliptic operators


Authors: Mu-Fa Chen and Feng-Yu Wang
Journal: Trans. Amer. Math. Soc. 349 (1997), 1239-1267
MSC (1991): Primary 35P15, 60H30
DOI: https://doi.org/10.1090/S0002-9947-97-01812-6
MathSciNet review: 1401516
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Abstract: A variational formula for the lower bound of the spectral gap of an elliptic operator is presented in the paper for the first time. The main known results are either recovered or improved. A large number of new examples with sharp estimate are illustrated. Moreover, as an application of the march coupling, the Poincaré inequality with respect to the absolute distribution of the process is also studied.


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Additional Information

Mu-Fa Chen
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, P.R. China
Email: mfchen@ns.bnu.edu.cn

Feng-Yu Wang
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, P.R. China

DOI: https://doi.org/10.1090/S0002-9947-97-01812-6
Keywords: Spectral gap, diffusion process, coupling
Received by editor(s): December 3, 1995
Additional Notes: Research supported in part by the National Natural Science Foundation of China and the Foundation of Institution of Higher Education for Doctoral Program
Article copyright: © Copyright 1997 American Mathematical Society