Related papers: G-Convergence, Dirichlet to Neumann maps and invis…
For a family of second-order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann functions, using Dirichlet and Neumann correctors. As a result we obtain asymptotic…
We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to…
Conformal invisibility devices are only supposed to work within the validity range of geometrical optics. Here we show by numerical simulations and analytical arguments that for certain quantized frequencies they are nearly perfect even in…
We consider approximate cloaking from a regularization viewpoint introduced in [13] for EIT and further investigated in [12] [17] for the Helmholtz equation. The cloaking schemes in [12] and [17] are shown to be (optimally) within…
In this paper we give results about projective embeddings of Riemann surfaces, smooth or nodal, which we apply to the inverse Dirichlet-to-Neumann problem and to the inversion of a Riemann-Klein theorem. To produce useful embeddings, we…
Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…
We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex…
We describe families of potentials which act as approximate cloaks for matter waves, i.e., for solutions of the time-independent Schr\"odinger equation at energy $E$, with applications to the design of ion traps. These are derived from…
In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this…
We propose a near-cloaking design which is a lamination of a finite number of layers of isotropic materials. The proposed design is an approximation of a cloaking material obtained by pushing forward a multi-coated structure for which the…
Simple applications of a principle of minimum energy and the property of monotonicity for the corresponding non-local operator, have allowed a direct proof of the G-compactness in a weak sense, as well as in the strong sense. The…
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…
In this paper, we study approximate cloaking for the Helmholtz equation in 3d where the cloaking device is based on transformations which blow up a cylinder of fixed height and small cross section of radius $\eps$ into the cloaked region.…
We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions…
We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition.…
We show that the decay of approximation numbers of compact composition operators on the Dirichlet space $\mathcal{D}$ can be as slow as we wish, which was left open in the cited work. We also prove the optimality of a result of…
For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…
We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence, or H-convergence, by means of the compensated compactness…
We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Neumann boundary condition in non-Lipschitz domains $\Omega \subset \mathbb C$. The suggested method is based on…
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…