Related papers: The Maxwell Compactness Property in Bounded Weak L…
We investigate regular elliptic boundary-value problems in bounded domains and show the Fredholm property for the related operators in an extended scale formed by inner product Sobolev spaces (of arbitrary real orders) and corresponding…
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 aim of this paper is to prove existence of weak solutions of hyperbolic-parabolic evolution inclusions defined on Lipschitz domains with mixed boundary conditions describing, for instance, damage processes and elasticity with inertia…
We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…
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 this paper the "strong" Maxwell operator defined on fields from the Sobolev space $W_2^1$, and the "weak" Maxwell operator defined on the natural domain are considered. It is shown that in a convex domain, and, more generally, in a…
We derive the asymptotic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field), in the exterior of the domain of influence of a compact set. This complements the previous well known results, restricted to…
This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…
We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…
We introduce a space of vector fields with bounded mean oscillation whose ``tangential'' and ``normal'' components to the boundary behave differently. We establish its Helmholtz decomposition when the domain is bounded. This substantially…
In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on…
Time-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the operators and the large, non-Hermitian linear systems resulting…
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…
We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and…
An inverse obstacle scattering problem for the wave governed by the Maxwell system in the time domain, in particular, over a finite time interval is considered. It is assumed that the electric field $\mbox{\boldmath $E$}$ and magnetic field…
We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability $\mu$ and the permittivity $\varepsilon$ are symmetric positive definite matrix-valued functions in $\mathbb{R}^{3}$. We show that a…