TY - JOUR
T1 - Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators
AU - Li , Yanyan
AU - Yang , Zhuolun
JO - Analysis in Theory and Applications
VL - 1
SP - 114
EP - 128
PY - 2021
DA - 2021/04
SN - 37
DO - http://doi.org/10.4208/ata.2021.pr80.12
UR - https://global-sci.org/intro/article_detail/ata/18767.html
KW - Conductivity problem, harmonic functions, maximum principle, gradient estimates.
AB - <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>