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Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators

Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators
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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.

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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.

Author Details

Yanyan Li

Zhuolun Yang

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