Related papers: Gradient Estimates for the Perfect and Insulated C…
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…
We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to…
We consider a boundary value problem for the conductivity equation in a bounded domain containing an inclusion which is nearly touching to the domain's boundary. We assume that the domain and the inclusion are disks with conductivity jump…
In this paper we study the {\it a priori} gradient estimates for admissible solutions to Neumann boundary value problem of fully nonlinear Hessian equations on Riemannian manifolds. We firstly derive an interior gradient estimates for…
In this paper, we will use the maximum principle to give a new proof of the gradient estimates for mean curvature equations with some oblique derivative problems. Specially, we shall give a new proof for the capillary problem with zero…
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 discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is…
We investigate a generalization of Calder\'on's problem of recovering the conductivity coefficient in a conductivity equation from boundary measurements. As a model equation we consider the p-conductivity equation with p strictly between…
The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our…
We deal with the problem of determining an inclusion within an electrical conductor from electrical boundary measurements. Under mild a priori assumptions we establish an optimal stability estimate.
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…
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…
We give upper and lower bounds of perturbation series for transition densities, corresponding to additive gradient perturbations satisfying certain space-time integrability conditions.
In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to Dirichlet and Neumann problems of a class of Schr\"odinger equations under the minimal…
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…
In conductor-insulator composites in which the conducting particles are dispersed in an insulating continuous matrix the electrical connectedness is established by interparticle quantum tunneling. A recent formulation of the transport…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
In this paper, we use the maximum principle to get the gradient estimate for the solutions of the prescribed mean curvature equation with Neumann boundary value problem, which gives a positive answer for the question raised by Lieberman…
We give explicit integral formulas for the solutions of planar conjugate conductivity equations in a circular domain of the right half-plane with conductivity $\sigma(x,y)=x^p$, $p\in\mathbb{Z}$. The representations are obtained via a…
This paper deals with higher gradient integrability for $\sigma$-harmonic functions $u$ with discontinuous coefficients $\sigma$, i.e. weak solutions of $\div(\sigma \nabla u) = 0$. We focus on two-phase conductivities, and study the higher…