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On Homogenization Of Elliptic Equations With Random Coefficients
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Joseph G. Conlon, University of Michigan
Ali Naddaf, University of Michigan
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Abstract
In this paper, we investigate the rate of convergence of the
solution $u_ve$ of the random elliptic
partial difference equation
$(nabla^{ve *} a(x/ve,om)nabla^ve+1)u_ve(x,om)=f(x)$
to the
corresponding homogenized solution. Here $xinveZ^d$, and
$ominOmega$
represents the randomness. Assuming that $a(x)$'s are
independent and uniformly
elliptic, we shall obtain an upper bound
$ve^alpha$ for the rate of convergence,
where $alpha$ is a
constant which depends on the dimension $dge 2$ and the deviation
of $a(x,om)$ from the identity matrix. We will also show that
the (statistical) average of
$u_ve(x,om)$ and its derivatives
decay exponentially for large $x$.
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Full text: PDF
Pages: 1-58
Published on: April 3, 2000
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Electronic Journal of Probability. ISSN: 1083-6489 |
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