Greensche tensoren und asymptotische gesetze der elektromagnetischen hohlraumschwingungen

Müller, Claus; Niemeyer, Horst

doi:10.1007/bf00250767

Cited by 31 publications

(10 citation statements)

References 11 publications

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“…His contributions provide the foundation on which almost all subsequent work is based. Low frequency asymptotics for Maxwell's boundary value problem have been given, for instance, by Müller and Niemeyer [22], Stevenson [38], Kleinman [11], Werner [50,51,52,53,55], Kress [12], Ramm [34], Kriegsmann and Reiss [13], Ramm, Weaver, Weck and Witsch [36], Athanasiadis, Costakis and Stratis [5] as well as by Picard [30] and Weck and Witsch [41]. We also should mention the book of Dassios and Kleinman [7].…”

Section: Introduction and Main Resultsmentioning

confidence: 87%

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Complete low frequency asymptotics for time-harmonic generalized Maxwell equations in nonsmooth exterior domains

Pauly¹

2008

Asymptotic Analysis

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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 of special 'polynomially growing' solutions of a corresponding static problem, which must be added to the 'usual' Neumann series in order to describe the low frequency asymptotic adequately. Partial integration yieldsand clearly all terms of the sum like M 2 C M ,η D q 1 J , 0 , 0,H + σ,m L 2,q,q+1 (Ω)

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Section: Introduction and Main Resultsmentioning

confidence: 87%

“…22 Let J ∈ N 0 and s, t, τ be as in the Main Theorem. Moreover, let (F, G) be an element of Reg q,0 s (Ω) .…”

mentioning

confidence: 99%

Complete low frequency asymptotics for time-harmonic generalized Maxwell equations in nonsmooth exterior domains

Pauly¹

2008

Asymptotic Analysis

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“…Since these eigenvectors are divergence free, we find ω 2 n E n = iω n rotB n = rot rotE n = −∆E n , n ∈ N, and likewise (∆ + ω 2 n )B n = 0. By elliptic regularity, E n , B n ∈ C ∞ (Λ, C 3 ), n ∈ N. The following asymptotics, which are uniform in x ∈ Λ, are proven in [25,Satz 12],…”

Section: 29])mentioning

confidence: 98%

Pauli-Fierz Type Operators with Singular Electromagnetic Potentials on General Domains

Matte

2017

Math Phys Anal Geom

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Abstract. We consider Dirichlet realizations of Pauli-Fierz type operators generating the dynamics of non-relativistic matter particles which are confined to an arbitrary open subset of the Euclidean position space and coupled to quantized radiation fields. We find sufficient conditions under which their domains and a natural class of operator cores are determined by the domains and operator cores of the corresponding Dirichlet-Schrödinger operators and the radiation field energy. Our results also extend previous ones dealing with the entire Euclidean space, since the involved electrostatic potentials might be unbounded at infinity with local singularities that can only be controlled in a quadratic form sense, and since locally square-integrable classical vector potentials are covered as well. We further discuss Neumann realizations of Pauli-Fierz type operators on Lipschitz domains.

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“…For the case of bounded smooth domains, this study goes back to [69] and we utilize both integral equation and Hilbert space techniques to extend the classical theory to this more general setting.…”

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confidence: 99%

Vector Potential Theory on Nonsmooth Domains in R3 and Applications to Electromagnetic Scattering

Mitrea¹,

Mitrea²,

Pipher³

1996

J Fourier Anal Appl

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We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.The main goal is to develop the corresponding theory for L p -integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering. Statement of the Problems and Introductory RemarksLet us consider the electromagnetic wave propagation in a homogeneous, isotropic medium that occupies the exterior of a bounded domain in R 3 and has electric conductivity σ ≥ 0, electric permittivity > 0, and magnetic permeability µ. If we denote by E, H the electric and the magnetic fields, respectively, and if J stands for the current density, then the Maxwell equations readAlso, in an isotropic conductor, the electric field satisfies Ohm's law σ E = J . An excellent exposition of this material can be found in [24, Vol. I]; cf. also [15].We assume time-harmonic dependency for E and H, that is, that for some time-independent vector fields E, H the following separation of variables holds:H(X, t) = µ − 1 2 H (X) e −iωt , P P

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Greensche tensoren und asymptotische gesetze der elektromagnetischen hohlraumschwingungen

Cited by 31 publications

References 11 publications

Complete low frequency asymptotics for time-harmonic generalized Maxwell equations in nonsmooth exterior domains

Complete low frequency asymptotics for time-harmonic generalized Maxwell equations in nonsmooth exterior domains

Pauli-Fierz Type Operators with Singular Electromagnetic Potentials on General Domains

Vector Potential Theory on Nonsmooth Domains in R3 and Applications to Electromagnetic Scattering

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