@Article{ATA-37-114,
author = {Li , Yanyan and Yang , Zhuolun},
title = {Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators},
journal = {Analysis in Theory and Applications},
year = {2021},
volume = {37},
number = {1},
pages = {114--128},
abstract = {<p style="text-align: justify;">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 $\beta &gt; 0$ when dimension $n \ge 3$. In this paper, we generalize the above results for insulators with flatter boundaries near touching points.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2021.pr80.12},
url = {http://global-sci.org/intro/article_detail/ata/18767.html}
}