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research
A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators
Authors
Mark P. Owen
Publication date
1 January 1998
Publisher
View
on
arXiv
Abstract
We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions
Ω
⊆
ℜ
N
\Omega\subseteq\real^N
Ω
⊆
ℜ
N
, where the order
2
m
2m
2
m
of the operator satisfies
N
<
2
m
N<2m
N
<
2
m
. 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
\Omega
Ω
. Work of Barbatis is applied to find the best constant in this expression.Comment: 29 pages, 6 diagram
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