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

1998/03/05 by Mark P. Owen, Owen, Mark P.
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.FA #math.SP #msc:35K25

paper · pdf · doi:10.48550/arxiv.math/9803014

29 pages, 6 diagrams

arxiv created 1998/03/05 · arxiv updated 2009/11/30

Abstract

We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions Ω⊆\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.

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