Related papers: Optimal gradient estimates for the insulated condu…
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…
For two neighbouring stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system of linear elasticity, may exhibit singular behavior as the distance between these two inclusions becomes arbitrarily small. In…
In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial…
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…
We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field $|J|$. We prove that the conductivity…
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…
We study the perfect conductivity problem with closely spaced perfect conductors embedded in a homogeneous matrix where the current-electric field relation is the power law $J=\sigma|E|^{p-2}E$. The gradient of solutions may be arbitrarily…
In this paper, we derive the pointwise upper bounds and lower bounds on the gradients of solutions to the Lam\'{e} systems with partially infinite coefficients as the surface of discontinuity of the coefficients of the system is located…
In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount $m>0$ of insulating material coating an insulated boundary part $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting…
A field in a homogeneous medium can be amplified or enhanced by inserting closely located perfectly conducting inclusions into the medium. In this paper precise quantitative estimates for such enhancement are derived when the given field is…
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…
If stiff inclusions are closely located, then the stress, which is the gradient of the solution, may become arbitrarily large as the distance between two inclusions tends to zero. In this paper we investigate the asymptotic behavior of the…
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth…
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…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises…
The numerical analysis of gradient inclusions in a compact subset of $2\times 2$ diagonal matrices is studied. Assuming that the boundary conditions are reached after a finite number of laminations and using piecewise linear finite…
This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…
We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike $\pm$ unit…