Related papers: Boundary determination of electromagnetic paramete…
For a semilinear elliptic equation, we prove uniqueness results in determining potentials and semilinear terms from partial Cauchy data on an arbitrary subboundary.
We prove for a two dimensional bounded domain that the Cauchy data for the Schroedinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential. This implies, for the conductivity equation, that if we…
In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs.…
This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique…
We study time-dependent acoustic and electromagnetic waves governed by the scalar wave equation or Maxwell's equations in a bounded three-dimensional domain. We establish the existence of time-dependent boundary excitations that can be…
In this article, we prove a variety of uniqueness results for ultrahyperbolic equations with general space and time dependent lower order terms. We address the problem of determining uniqueness of solutions from boundary data as well as…
Maxwell's equations are solved when the amplitude and phase of the electromagnetic field are determined at all points in space. Generally, the Stokes parameters can only capture the amplitude and polarization state of the electromagnetic…
We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our…
We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is…
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…
In the current paper we consider an inverse boundary value problem of electromagnetism with nonlinear Second Harmonic Generation (SHG) process. We show the unique determination of the electromagnetic material parameters and the SHG…
We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type…
We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…
We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in $\R^n$, $n\ge 3$, for the magnetic Schr\"odinger operator with $L^\infty$ magnetic and electric potentials determines the magnetic field and…
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…
The article deals with electrodynamics in the presence of anisotropic materials having scalar wave impedance. Maxwell's equations written for differential forms over a 3-manifold are analysed. The system is extended to a Dirac type first…
We establish the global-in-time existence and uniqueness of classical solutions to the "one and one-half" dimensional relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely…