Related papers: Cloaking for a quasi-linear elliptic partial diffe…
A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
In this paper we introduce a new type of symmetrization, which preserves the anisotropic perimeter of the level sets of a suitable concave smooth function, in order to prove sharp comparison results for solutions of a class of homogeneous…
We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a…
In this paper, we study the nonhomogeneous Dirichlet problem concerning general semilinear elliptic equations in divergence form. We establish that the boundary Lipschitz regularity of solutions under some more weaker conditions on the…
Let $\Omega $ be a bounded domain in $\mathbb{R}^{d}$ $\left( d\geq 2\right) $ pretty regular. We solve the variational Dirichlet problem for a class of quasi-linear elliptic systems.
In this work, we are interested in to study removability of a singular set in the boundary for some classes of quasilinear elliptic equations. We will approach this question in two different ways: through an asymptotic behavior at the…
A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
We introduce a class of conformal versions of the previously introduced quasi-conformal carpet cloak, and show how to construct such conformal cloaks for different cloak shapes. Our method provides exact refractive-index profiles in closed…
Cloaking is typically reciprocal. We introduce here the concept of \emph{transmittable nonreciprocal cloaking} whereby the cloaking system operates as a standard omnidirectional cloak for external illumination, but can transmit light from…
For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the…
Based on the transformation optics, a novel transmission-line (TL) approach to realize invisibility cloaking using planar anisotropic metamaterials (MTMs) is proposed. The two-dimensional cylindrical cloaks are modeled based on…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
The ability to control electromagnetic fields, heat currents, electric currents, and other physical phenomena by coordinate transformation methods has resulted in novel functionalities, such as cloaking, field rotations, and concentration…
Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.
Invisibility cloaking imposes strict conditions on the refractive index profiles of cloaking media that must be satisfied to successfully hide an object. The first experimental demonstrations of cloaking used artificial metamaterials to…
We study two types of asymptotic problems whose common feature - and difficulty- is to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
The unique determination of electrical conductivity is extensively studied for isotropic conductivity ever since Calderon's suggestion of the EIT (Electrical Impedance Tomography) problem. However, it is known that there are many…