Affiliation:
1. Beijing Computational Science Research Center , Beijing 100193, China
Abstract
We consider an insulated conductivity model with two neighboring inclusions of m-convex shapes in Rd when m ≥ 2 and d ≥ 3. We establish pointwise gradient estimates for the insulated conductivity problem and capture the gradient blow-up rate of order ɛ−1/m+β with β=[−(d+m−3)+(d+m−3)2+4(d−2)]/(2m)∈(0,1/m) as the distance ɛ between these two insulators tends to zero. In particular, the optimality of the blow-up rate is also demonstrated for a class of axisymmetric m-convex inclusions.
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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1. Gradient estimates for the insulated conductivity problem with inclusions of the general m‐convex shapes;ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik;2023-08-02