Related papers: Blowup Analysis for the Perfect Conductivity Probl…
In the perfect conductivity problem of composite material, the electric field concentrates in a narrow region in between two inclusions and always becomes arbitrarily large when the distance between inclusions tends to zero. To characterize…
When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbitrary large. We establish both the pointwise upper bound and…
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 the perfect conductivity problem of composites, the electric field may become arbitrarily large as $\varepsilon$, the distance between the inclusions and the matrix boundary, tends to zero. The main contribution of this paper lies in…
We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb{R}^n$. It was known that in the setting of strictly convex inclusions, the gradient of solutions may blow up as the distance between…
We consider the conductivity problem in the presence of adjacent circular inclusions having arbitrary constant conductivity. When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the…
We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension…
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…
It is interesting to study the stress concentration between two adjacent stiff inclusions in composite materials, which can be modeled by the Lam\'e system with partially infinite coefficients. To overcome the difficulty from the lack of…
The purpose of this paper is to set out optimal gradient estimates for solutions to the isotropic conductivity problem in the presence of adjacent conductivity inclusions as the distance between the inclusions goes to zero and their…
We consider a gradient estimate for a conductivity problem whose inclusions are two neighboring insulators in three dimensions. When inclusions with an extreme conductivity (insulators or perfect conductors) are closely located, the…
We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We…
We study the insulated conductivity problem which involves two adjacent convex insulators embedded in a bounded domain. It is known that the gradient of solutions may blow up as the distance between the two inclusions tends to zero.…
This paper concerns optimal gradient estimates of solutions for the perfect conductivity problem with closely spaced interfacial boundaries. The problem arises from composite material. Our estimates exhibit different blow up rates of the…
When inclusions with extreme conductivity (insulator or perfect conductor) are closely located, the gradient of the solution to the conductivity equation can be arbitrarily large. And computation of the gradient is extremely challenging due…
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…
When two perfectly conducting inclusions are located closely to each other, the electric field concentrates in a narrow region in between two inclusions, and becomes arbitrarily large as the distance between two inclusions tends to zero.…
In this paper, we investigate the gradient estimates for solutions to the perfect conductivity problem with two closely spaced perfect conductors embedded in a homogeneous matrix, modeled by $p$-Laplacian elliptic equations. We first prove…
This paper studies field concentration between two nearly touching conductors separated by imperfect low-conductivity interfaces, modeled by Robin boundary conditions. It is known that for any sufficiently small interfacial bonding…
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…