Journal of Operator Theory

Volume 41, Issue 1, Winter 1999 pp. 93-120.

A Riemannian off-diagonal heat kernel bound for uniformly elliptic operators

Authors: Mark P. Owen
Author institution: Department of Mathematics, King's College London, Strand, London WC2R 2LS, England

Summary: We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions

$\Omega \subseteq\real^N$ , where the order

$2m$ of the operator satisfies

$N<2m$ . The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on

$\Omega$ . Work of Barbatis~([1]) is applied to find the best constant in this expression.

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