Related papers: Boundary determination of electromagnetic paramete…
When a (frequency-domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the…
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem that remains open, and one approach to explaining its origins is the so-called Exclusivity principle, relying on probabilistic assumptions…
We study the effect of the parameter $\lambda$, the dimension $N$, the profile $f$ and the geometry of the domain $\Omega \subset\mathbb{R}^N$, on the question of uniqueness of the solutions to the following elliptic boundary value problem…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present $H^2$-norm bound and other high-order norm bounds for strong solutions. The $H^2$-estimate have been derived in [M. Dauge, M. Costabel and…
In this paper we study the uniqueness and the increasing stability in the inverse source problem for electromagnetic waves in homogeneous and inhomogeneous media from boundary data at multiple wave numbers. For the unique determination of…
We describe arithmetic cross-sections for geodesic flow on compact surfaces of constant negative curvature using generalized Bowen-Series boundary maps and their natural extensions associated to cocompact torsion-free Fuchsian groups. If…
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
While doing electromagnetic analysis using FEM (Finite element method), if we can implement the underlying symmetric nature of the problem, there will be significant reduction in the computational cost. Symmetric nature of the problem can…
We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$…
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
The article contains the results of the author's recent investigations of rigidity problems of domains in Euclidean spaces carried out for developing a new approach to the classical problem of the unique determination of bounded closed…
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(\Omega)$-norm with order $1/2$ in convex…
Today's textbooks of electromagnetism give the particular solution to Maxwell's equations involving the integral over the charge and current sources at retarded times. However, the texts fail to emphasize the role played by the choice of…
The procedure for obtaining a difference equation, the solution of which is the components of the electric (or magnetic) field at the chosen set of volume points of the resonator chain, was developed. We started with the wave equation with…
Via Carleman estimates we prove uniqueness and continuous dependence results for lateral Cauchy problems for linear integro-differential parabolic equations without initial conditions. The additional information supplied prescribes the…
We prove a magnetic version of the Maz'ya-Shaposhnikova singular limit of nonlocal norms with vanishing fractional parameter. This complements a general convergence result recently obtained by authors when the parameter approaches one.
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…