Related papers: Uniqueness Theorem: With Normal Components Specifi…
The linearized field equations of general relativity in harmonic coordinates are given by an inhomogeneous wave equation. In the region exterior to the matter field, the retarded solution of this wave equation can be expanded in terms of 10…
We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition…
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…
We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…
The Floquet-Bloch theorem allows waves in infinite, lossless periodic media to be expressed as a sum of discrete Floquet-Bloch modes, but its validity is challenged under the realistic constraints of loss and finite extent. In this work, we…
These notes are intended as an introduction to the question of unique continuation for the wave operator, and some of its applications. The general question is whether a solution to a wave equation in a domain, vanishing on a subdomain has…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well…
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite point-vector fields with discrete and localized point interactions. These fields are taken as a…
This article is devoted to the kinetic description in phase space of magnetically confined plasmas. It addresses the problem of stability near equilibria of the Relativistic Vlasov Maxwell system. We work under the Glassey-Strauss compactly…
We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the…
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive…
This paper presents a new single-source surface integral equation (SS-SIE) to model composite penetrable objects. In the proposed formulation, the surface electric and magnetic fields on all interior boundaries are first eliminated through…
We argue that the classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the…
We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite…
We clarify some arguments concerning Jefimenko's equations, as a way of constructing solutions to Maxwell's equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial…
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
If a set of charged objects collide in space and the fragments disperse, then this process will emit electromagnetic waves. Classical soft photon theorem determines the constant term and the leading power law fall-off of the wave-form at…
We present a complete theory of electromagnetic modes in spherical cavities, resolving fundamental questions about the nature of angular quantization. The standard result that angular indices $(\ell,m)$ must be integers is shown to be a…