Related papers: Strichartz estimates for Maxwell equations in medi…
This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method…
We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…
We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single…
The Maxwell equations and the constitutive relations describe the classical propagation of electromagnetic waves in continuous matter. Here, we investigate the effects stemming from extended constitutive relations on the propagation of…
We analyse the behaviour of the spectrum of the system of Maxwell equations of electromagnetism, with rapidly oscillating periodic coefficients, subject to periodic boundary conditions on a "macroscopic" domain $(0,T)^d, T>0.$ We consider…
The purpose of this paper is to establish a complete Schauder theory for the second-order linear elliptic equation and the time-harmonic Maxwell's system. We prove global H\"older regularity for the solutions to the time-harmonic…
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates…
Multiple vertical fracture sets, combined with horizontal fine layering produce an equivalent medium of orthorhombic or monoclinic symmetry. This is particularly important in fracture reservoir characterization. Fractured reservoirs are…
We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand…
We give stability estimates in the Cauchy problem for general partial differential equation of the elliptic type similar to the Helmholtz equation. We do not impose any (pseudo)convexity assumptions on the domain or the operator. These…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see…
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards…
The Maxwell equations for chiral media are treated with the aid of quaternionic analysis methods. Besides the possibility of simplification of the form of such basic facts like the Stratton-Chu formulas we obtain a criterion for the…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive…
In the thesis at hand we give a comprehensive discussion of basic problems for generalized Maxwell equations with mixed boundary conditions using the calculus of alternating differential forms on Riemannian manifolds of arbitrary dimension.…
It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal…
The equations for the electromagnetic field in an anisotropic media are written in a form containing only the transverse field components relative to a half plane boundary. The operator corresponding to this formulation is the…