Owen M.P.
A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators
(661K, Postscript)
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.