相关论文: A few results on permittivity variations in electr…
Applying the method of characteristics leads to wavefunctions and dynamic localization conditions for electrons on the one dimensional lattice under perpendicular time dependent electric and magnetic fields. Such conditions proceed again in…
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In…
We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…
After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
We present a simple gedanken experiment in which a compact object traverses a spacetime with three macroscopic spatial dimensions and $n$ compact dimensions. The compactification radius is allowed to vary, as a function of the object's…
The present paper shows that the eigenvalue sequence $\{\lambda_n(q)\}_{n\geqslant 1}$ of regular Sturm-Liouville eigenvalue problem with certain monotonic weights is uniformly Lipschitz continuous with respect to the potential $q$ on any…
We study analytic spectral perturbation theory for the time-harmonic Maxwell operator in a perfectly electrically conducting cavity containing a high-contrast core--shell structure. The dielectric permittivity equals $1$ in a bounded…
In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like $RCD(K,N)$-spaces, every Sobolev function with local $L^{p}$-Laplacian and $p>\dim\mu$ is locally…
Let $M$ be the interior of a connected, oriented, compact manifold $V$ of dimension at least 2. If each path component of $\partial V$ has amenable fundamental group, then we prove that the simplicial volume of $M$ is equal to the relative…
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…
In this paper we prove uniqueness for an inverse boundary value problem (IBVP) arising in electrodynamics. We assume that the electromagnetic properties of the medium, namely the magnetic permeability, the electric permittivity and the…
A small dielectric object with positive permittivity may resonate when the free-space wavelength is large in comparison with the object dimensions if the permittivity is sufficiently high. We show that these resonances are described by the…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…
We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on…
The ordered eigenvalues define a Lipschitz map on the real vector space of Hermitian $d \times d$ matrices. We prove that this map acts continuously, but not uniformly continuously, by superposition on the Sobolev spaces $W^{1,q}$, for all…
The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in…
In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic…