A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators

Details A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators

1998-03-05

arxiv.org/abs/math/9803014v1

Mathematics

Spectral Theory

29 pages, 6 diagrams

Scientific paper

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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