相关论文: A limiting absorption principle for Helmholtz syst…

We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H\"older assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In…

We study homogenization problem for the stationary Maxwell system. It is supposed that the magnetic permeability and the dielectric permittivity locally close to fast-oscillating (with respect to some small parameter) periodic functions…

The study of the limiting absorption principle for elliptic equations with periodic structures is very challenging when the dimension is greater than 1. The fundamental reason for the dimensional barrier is the mismatch between directional…

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…

We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell…

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…

We show weighted non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let $p,q \in (1,\infty)$ and we…

Absorbing boundary conditions are presented for three-dimensional time-dependent Schr\"odinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a…

Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual…

A theory of the absorption of a laser field by an atomic or condensed matter medium is presented for the case where the medium is also interacting with a strong electromagnetic field. The rotating wave approximation is not assumed for the…

The optimal $L^p \to L^q$ mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the…

We consider a Maxwell system on $\mathbb{R}^3$ with periodic and highly oscillating coefficients. It is known that the solutions converge in the weak-$\ast$ topology of $L^\infty(0,T;\,L^2(\mathbb{R}^3))$ to the solution of a similar…

We study the Rellich type theorem (RT) for the Maxwell operator $\hat H^D=\hat D\hat H_0$ on ${\bf Z}^3$ with constant anisotropic medium, i.e. the permittivity and permeability of which are non-scalar constant diagonal matrices. We also…

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum…

We prove that the noncommutative Lorentz norm (associated to a semifinite von Neumann algebra) of a propagator of the form $\varphi(|\mathscr{L}|)$ can be estimated if the modulus of the Borel function $\varphi$ is bounded by a continuous…

In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown…

We study a limiting absorption principle for the boundary-value problem describing a hybrid plasma resonance, with a regular coefficient in the principal part of the operator that vanishes on a curve inside the domain and changes its sign…

Pseudo-Hermitian operators appear in the solution of Maxwell's equations for stationary non-dispersive media with arbitrary (space-dependent) permittivity and permeability tensors. We offer an extension of the results in this direction to…

We consider the Dirichlet Laplacian in the half-plane with constant magnetic field. Due to the translational invariance this operator admits a fiber decomposition and a family of dis- persion curves, that are real analytic functions. Each…