# The Maxwell operator with periodic coefficients in a cylinder

@article{Filonov2018TheMO,
title={The Maxwell operator with periodic coefficients in a cylinder},
author={Nikolai Filonov and Andrei Prokhorov},
journal={St. Petersburg Mathematical Journal},
year={2018}
}
• Published 31 January 2018
• Mathematics
• St. Petersburg Mathematical Journal
In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is absolutely continuous.
3 Citations

### The absence of eigenvalues for certain operators with partially periodic coefficients

• N. Filonov
• Computer Science
St. Petersburg Mathematical Journal
• 2022
The Schrödinger operator in the Euclidean space whose potential is periodic in some variables and decays in the remaining variables faster than power is proved.

## References

SHOWING 1-10 OF 12 REFERENCES

### The absolute continuity of the spectrum of Maxwell operator in a periodic media

We prove that the spectrum of Maxwell operator, (B,E)⟼(−rot(E),a(x)rot(b(x)B)), with non-negative and periodic functions a(x) and b(x), is absolutely continuous.

### Absolutely Continuous Spectrum for the Isotropic Maxwell Operator with Coefficients that are Periodic in Some Directions and Decay in Others

• Mathematics
• 2005
The purpose of this paper is to prove that the spectrum of an isotropic Maxwell operator with electric permittivity and magnetic permeability that are periodic along certain directions and tending to

### Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder

We consider the periodic Schrödinger operator on a d-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form σ(x, y)δΣ(x,y), where Σ is a

### Nonunique continuation for the Maxwell system

An example of the stationary Maxwell system, which has a nontrivial smooth solution with a compact support is given; the coefficients ε and μ belong to Cα for all α < 1. Our example shows that the

### Regularity of Electromagnetic Fields in Convex Domains

• Mathematics
• 2015
In this paper, a “strong” Maxwell operator defined on fields from the Sobolev space W21, and a “weak” Maxwell operator defined on the natural domain are considered. It is shown that in a convex

### Absolute Continuity of the Spectrum of the Periodic Maxwell Operator in a Layer

AbstractThe Maxwell operator in a layer $${\mathbb{R}}^2 \times \left( {0,T} \right)$$ is studied. It is assumed that the electric permittivity μ(x) and the magnetic permeability ε(x)are periodic

### Absence of the singular continuous component in spectra of analytic direct integrals

• Mathematics
• 2006
We give a simple proof of the absence of the singular continuous component in spectra of self-adjoint operators that are representable as analytic direct integrals. Bibliography: 7 titles.

### Floquet Theory for Partial Differential Equations

CONTENTSIntroduction Chapter I. Preparatory results ??1. The cokernel of a Fredholm morphism in spaces of sections ??2. The cokernel of a Fredholm morphism in spaces of sections with bounds Chapter

• Anal. Appl
• 2013

### The selfadjoint Maxwell operator in arbitrary domains, Algebra i Analiz

• (Russian). English translation in: Leningr. Math. J. 1,
• 1989