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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Poincaré Type Inequalities


Authors: Roger Chen and Peter Li
Journal: Trans. Amer. Math. Soc. 349 (1997), 1561-1585
MSC (1991): Primary 35P15, 58G11, 58G25
MathSciNet review: 1401517
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Abstract: Using estimates of the heat kernel we prove a Poincaré inequality for star-shape domains on a complete manifold. The method also gives a lower bound for the gap of the first two Neumann eigenvalues of a Schrödinger operator.


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Additional Information

Roger Chen
Affiliation: Department of Mathematics, National Cheng Kung University, Tainan, Taiwan
Email: rchen@mail.ncku.edu.tw

Peter Li
Affiliation: Department of Mathematics, University of California, Irvine, California 92717-3875
Email: pli@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01813-8
PII: S 0002-9947(97)01813-8
Received by editor(s): October 12, 1995
Additional Notes: The second author’s research was partially supported by NSF grant DMS-9300422
Article copyright: © Copyright 1997 American Mathematical Society