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

摘要

We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions #OMEGA# is contained in R~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.