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Seventh Mississippi State - UAB Conference on Differential Equations & Computational Simulations
November 1-3, 2007
Doubletree Hotel
Birmingham, AL, USA |
|
Organizers
Mississippi State University & University of Alabama - Birmingham
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Gradient Estimates for the Perfect Conductivity Problem
by
Ellen Shiting Bao
Rutgers University
Coauthors: YanYan Li, Biao Yin
Abstract
We consider the optimal bound on the stress occurring between a pair
of closely spaced fibers in a bounded domain. With Dirichlet
boundary condition, the conductivity problem can be described as
follows
|
div |
ì
í
î
|
|
é
ë
|
1+c(D1∪D2)(k-1) |
ù
û
|
∇uk |
ü
ý
þ
|
=0 in W, |
|
where W contains two inclusions D1 and D2 which are
e-apart, and ∇uk represents the stresses.
We study the perfect conductivity problem, where k=+∞. We
provide an optimal blow-up rate of the gradient estimate as the
separation distance e approaches 0. It is shown that the
blow-up rate depends not only on the dimension, but also on the
shape of the inclusions.
PDF
Date received: August 31, 2007
Copyright © 2007 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cauf-90.