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On Homogenization Of Elliptic Equations With Random Coefficients


 
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1. Title Title of document On Homogenization Of Elliptic Equations With Random Coefficients
 
2. Creator Author's name, affiliation, country Joseph G. Conlon; University of Michigan
 
2. Creator Author's name, affiliation, country Ali Naddaf; University of Michigan
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Homogenization, elliptic equations, random environment, Euler-Lagrange equation.
 
3. Subject Subject classification 35R60, 60J75
 
4. Description Abstract In this paper, we investigate the rate of convergence of the solution $u_\varepsilon$ of the random elliptic partial difference equation $(\nabla^{\varepsilon *} a(x/\varepsilon,\omega)\nabla^\varepsilon+1)u_\varepsilon(x,\omega)=f(x)$ to the corresponding homogenized solution. Here $x\in\varepsilon Z^d$, and $\omega\in\Omega$ represents the randomness. Assuming that $a(x)$'s are independent and uniformly elliptic, we shall obtain an upper bound $\varepsilon^\alpha$ for the rate of convergence, where $\alpha$ is a constant which depends on the dimension $d\ge 2$ and the deviation of $a(x,\omega)$ from the identity matrix. We will also show that the (statistical) average of $u_\varepsilon(x,\omega)$ and its derivatives decay exponentially for large $x$.
 
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7. Date (YYYY-MM-DD) 2000-04-03
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/65
 
10. Identifier Digital Object Identifier 10.1214/EJP.v5-65
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 5
 
12. Language English=en en
 
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