97-422 Owen M.P.
A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators (661K, Postscript) Jul 25, 97
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Abstract. 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 is applied to find the best constant in this expression.

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