Related papers: The Maxwell Compactness Property in Bounded Weak L…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…
In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…
Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…
We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…
In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.
The behaviour of the Maxwell field near one of the spatial infinities of the Schwarzschild solution is analysed by means of the transport equations implied by the Maxwell equations on the cylinder at spatial infinity. Initial data for the…
We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…
For Maxwell operators $(E,H) \to (i \epsilon^{-1} \nabla\times H, -i \mu^{-1} \nabla \times E)$ in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance and Leontovich boundary…
In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…
The effect of gravity in Maxwell's equations is often treated as a medium property. The commonly used formulation is based on managing Maxwell's equations in exactly the same form as in Minkowski spacetime and expressing the effect of…
The time local and global well-posedness for the Maxwell-Schr{\"o}dinger equations is considered in Sobolev spaces in three spatial dimensions. The Strichartz estimates of Koch and Tzvetkov type are used for obtaining the solutions in the…
We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
We investigate the existence of solutions of constrained nonlinear differential inclusions with nonlocal boundary conditions. Our viability theorems are based on the assumption that the right-hand side of differential inclusion is defined…
A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
We analyse how the spectrum of the anisotropic Maxwell system with bounded conductivity on a Lipschitz domain is approximated by domain truncation. First we prove a new non-convex enclosure for the spectrum of the Maxwell system, with weak…