Gradient estimates of solutions to the insulated conductivity problem in dimension greater than two

DOI10.1007/S00208-022-02368-XarXiv2012.14056MaRDI QIDQ6357042

Yanyan Li, Zhuolun Yang

Publication date: 27 December 2020

Abstract: We study the insulated conductivity problem with inclusions embedded in a bounded domain in $mathbb{R}^n$. The gradient of solutions may blow up as $varepsilon$, the distance between inclusions, approaches to $0$. An upper bound for the blow up rate was proved to be of order $varepsilo{n}^{-1/2}$. The upper bound was known to be sharp in dimension $n=2$. However, whether this upper bound is sharp in dimension $nge3$ has remained open. In this paper, we improve the upper bound in dimension $nge3$ to be of order $$, for some $$.

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) A priori estimates in context of PDEs (35B45) Blow-up in context of PDEs (35B44)

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