Related papers: Gradient estimates for the conductivity problem wi…
We consider a family of optimal control problems in the plane with dynamics and running costs possibly discontinuous across an oscillatory interface $\Gamma_\epsilon$. The oscillations of the interface have small period and amplitude, both…
We consider the diffusive Hamilton-Jacobi equation $$u_t-\Delta u=|\nabla u|^p,$$ with Dirichlet boundary conditions in two space dimensions, which arises in the KPZ model of growing interfaces. For $p>2$, solutions may develop gradient…
In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with…
We analyse the effect of a Signorini-type interface condition on the asymptotic behaviour, as {\epsilon} tends to zero, of a problem posed in an open bounded cylinder of {R^N}, {N\geq 2}, divided in two connected components by an imperfect…
Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be \sigma=\sigma_0(1+0.01 g), where 'g' is the dimensionless ("fine structure") coupling constant. The…
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…
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…
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…
We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate…
The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal-insulator…
The least gradient problem (minimizing the total variation with given boundary data) is equivalent, in the plane, to the Beckmann minimal-flow problem with source and target measures located on the boundary of the domain, which is in turn…
We present a quantum analysis of the massless excitations in graphene with a charge impurity. When the effective charge exceeds a certain critical value, the spectrum is quantized and is unbounded from below. The corresponding eigenstates…
We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the…
The Thouless conjecture states that the average conductance of a disordered metallic sample in the diffusive regime can be related to the sensitivity of the sample's spectrum to a change in the boundary conditions. Here we present results…
The "chemical bond" is a central concept in molecular sciences, but there is no consensus as to what a bond actually is. Therefore, a variety of bonding models have been developed, each defining the structure of molecules in a different…
Certain classes of electromagnetic boundaries satisfying linear and local boundary conditions can be defined in terms of the dispersion equation of waves matched to the boundary. A single plane wave is matched to the boundary when it…
The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the…
This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally,…
The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect…
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…