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

We study minimisation problems in $L^\infty$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear…

We prove uniform $L^p$ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators on…

We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to higher dimensional noncommutative tori and operator valued…

Let $$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj}, \quad x\in\Rn,$$ be a constant coefficient first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous…

In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not…

We prove the limiting absorption principle on the non-compact interval $I$, on which the uniformly positive Mourre estimate holds. We reveal that such a result yields so-called smoothing estimates.

We study the following Helmholtz equation $$ (\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + \lambda u = f(x) $$ in $\mathbb{R}^d$ with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the…

In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…

We regard anisotropic Maxwell's equations as a boundary control and observation system on a bounded Lipschitz domain. The boundary is split into two parts: one part with perfect conductor boundary conditions and the other where the control…

In this work we present a derivation of the real-time time-dependent orbital-optimized M{\o}ller-Plesser TDOMP2 and its biorthogonal companion, time-dependent non-orthogonal OMP2 (TDNOMP2), theory starting from the time-dependent…

The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…

We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby, we identify degenerate operators in terms…

We give an elementary proof of Burq's resolvent bounds for long range semiclassical Schroedinger operators. Globally, the resolvent norm grows exponentially in the inverse semiclassical parameter, and near infinity it grows linearly. We…

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 consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…

We obtain $L^p(L^q)$ maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.

We study real resonances and embedded eigenvalues of the Kramers--Fokker--Planck operator with a long-range potential. We prove that thresholds are only possible accumulation points of eigenvalues and that the limiting absorption principle…

We prove a uniform weighted resolvent estimate for the massless Klein-Gordon operator on a curved spacetime which is sufficiently close to the Minkowski spacetime. This particularly implies the existence and H\"{o}lder continuity of the…

It is well known that when the geometry and/or coefficients allow stable trapped rays, the outgoing solution operator of the Helmholtz equation (a.k.a. the resolvent of the Laplacian) grows exponentially through a sequence of real…

This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present $H^2$-norm bound and other high-order norm bounds for strong solutions. The $H^2$-estimate have been derived in [M. Dauge, M. Costabel and…