Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions

Details Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions

2009-09-22

arxiv.org/abs/0909.3901v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in $\mathbb{R}^n, n\ge 2$. For these two extreme cases of the conductivity problems, the gradients of their solutions may blow up as two inclusions approach each other. We establish the gradient estimates for the perfect conductivity problems and an upper bound of the gradients for the insulated conductivity problems in terms of the distances between any two closely spaced inclusions.

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