Year: 2021
Author: Yanyan Li, Zhuolun Yang
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 114–128
Abstract
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. When the distance of inclusions, denoted by $\varepsilon$, goes to 0, the gradient of solutions may blow up. When two inclusions are strictly convex, it was known that an upper bound of the blow-up rate is of order $\varepsilon^{-1/2}$ for $n = 2$, and is of order $\varepsilon^{-1/2 + \beta}$ for some $\beta > 0$ when dimension $n \ge 3$. In this paper, we generalize the above results for insulators with flatter boundaries near touching points.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2021.pr80.12
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 114–128
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Conductivity problem harmonic functions maximum principle gradient estimates.
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