Related papers: Inverse problems for Maxwell's equations in a slab…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
In this paper, we extend and simplify the methods in [13] to improve the results on uniqueness of the boundary determination for the Maxwell equation. In particular, we show that the electromagnetic parameters are uniquely determined to…
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is…
In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We…
Two recently derived integral equations for the Maxwell transmission problem are compared through numerical tests on simply connected axially symmetric domains for non-magnetic materials. The winning integral equation turns out to be…
We survey recent results on inverse boundary value problems for the magnetic Schroedinger equation.
We solve time-harmonic Maxwell's equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction-extension estimates for perturbations…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
Time-varying materials bring an extra degree of design freedom compared to their conventional time-invariant counterparts. However, few discussions have focused on the underlying physical difference between spatial and temporal boundaries.…
We prove resolvent estimates in $L^p$-spaces for time-harmonic Maxwell's equations in two spatial dimensions and in three dimensions in the partially anisotropic case. In the two-dimensional case the estimates are sharp up to endpoints. We…
We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater…
We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…