Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators
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 Rn. When the distance of inclusions, denoted by ε, 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 ε−1/2 for n=2, and is of order ε−1/2+β for some β>0 when dimension n≥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.
Author Details
Yanyan Li Email
Zhuolun Yang Email
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