2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76666We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions $Ω\subseteq\real^N$, 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 $Ω$. Work of Barbatis is applied to find the best constant in this expression.29 pages, 6 diagramsSpectral TheoryFunctional Analysis35K25text