On Poincaré Type Inequalities

Chen, Roger; Li, Peter

doi:10.1090/S0002-9947-97-01813-8

On Poincaré Type Inequalities
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by Roger Chen and Peter Li

Trans. Amer. Math. Soc. 349 (1997), 1561-1585

DOI: https://doi.org/10.1090/S0002-9947-97-01813-8

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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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