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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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