On Homogenization Of Elliptic Equations With Random Coefficients
Joseph G. Conlon, University of Michigan
Ali Naddaf, University of Michigan
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 $x$.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.