Related papers: The Optimal Gradient Estimates for Perfect Conduct…
In this paper we study the boundary gradient estimate of the solution to the insulated conductivity problem with the Neumann boundary data when a convex insulating inclusion approaches the boundary of the matrix domain. The gradient of…
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We…
In composite materials, the inclusions are frequently spaced very closely. The electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusions will always become arbitrarily large. In this paper, we…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
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 $0$. It was known that the…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb R^n$, for $n \ge 3$. The gradient of solutions may blow up as $\varepsilon$, the distance between inclusions, approaches to $0$. We…
We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the…
In composite material, the stress may be arbitrarily large in the narrow region between two close-to-touching hard inclusions. The stress is represented by the gradient of a solution to the Lam\'{e} system of linear elasticity. The aim of…
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…
A high-contrast two-phase nonlinear composite material with adjacent inclusions of $m$-convex shapes is considered for $m>2$. The mathematical formulation consists of the insulated conductivity problem with $p$-Laplace operator in…
In this paper we analyze the gradient blow-up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core-shell geometry. Assuming that the core and shell have circular boundaries that…
In this paper, we are concerned with the gradient estimate of the electric field due to two nearly touching dielectric inclusions, which is a central topic in the theory of composite materials. We derive accurate quantitative…
We study the gradient and higher order derivative estimates for the transmission problem in the presence of closely located inclusions. We show that in two dimensions, when relative conductivities of circular inclusions have different…
In the region between close-to-touching hard inclusions, the stress may be arbitrarily large as the inclusions get closer. The stress is represented by the gradient of a solution to the Lam\'e system of linear elasticity. We consider the…
We consider the insulated conductivity problem with two unit balls as insulating inclusions, a distance of order $\varepsilon$ apart. The solution $u$ represents the electric potential. In dimensions $n \ge 3$ it is an open problem to find…
This paper deals with the field enhancement, that is, the gradient blow-up, due to presence of a bow-tie structure of perfectly conducting inclusions in two dimensions. The bow-tie structure consists of two disjoint bounded domains which…
If two conducting or insulating inclusions are closely located, the gradient of the solution may become arbitrarily large as the distance between inclusions tends to zero, resulting in high concentration of stress in between two inclusions.…
In high-contrast elastic composites, it is vitally important to investigate the stress concentration from an engineering point of view. The purpose of this paper is to show that the blowup rate of the stress depends not only on the shape of…
The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. Much attention has been devoted to the blow-up estimate, especially in two dimensions, for the…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…