The Maxwell operator with periodic coefficients in a cylinder. (English. Russian original) Zbl 1398.35228
St. Petersbg. Math. J. 29, No. 6, 997-1006 (2018); translation from Algebra Anal. 29, No. 6, 182-196 (2017).
Summary: The object of study is the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of the cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is absolutely continuous.
MSC:
| 35Q61 | Maxwell equations |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35P05 | General topics in linear spectral theory for PDEs |
References:
| [1] | BS89 M. Sh. Birman and M. Z. Solomyak, The selfadjoint Maxwell operator in arbitrary domains, Algebra i Analiz 1 (1989), no. 1, 96-110; English transl., Leningrad Math. J. 1 (1990), no. 1, 99-115. · Zbl 0733.35099 |
| [2] | D M. N. Demchenko, On the nonuniqueness of the continuation of the solution of the Maxwell system, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 393 (2011), 80-100; English transl., J. Math. Sci. (N.Y.) 185 (2012), no. 4, 554-566. · Zbl 1259.78008 |
| [3] | FKl N. Filonov and F. Klopp, Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others, Comm. Math. Phys. 258 (2005), 75-85. · Zbl 1082.35114 |
| [4] | FP A. Prohorov and N. Filonov, Regularity of electromagnetic fields in convex domains, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 425 (2014), 55-85; English transl., J. Math. Sci. (N.Y.) 210 (2015), no. 6, 793-813. · Zbl 1360.35265 |
| [5] | FilSob N. Filonov and A. V. Sobolev, Absence of the singular continuous component in the spectrum of analytic direct integrals, Zap. Nauch. Sem. S.-Peterburg. Otdel. Math. Inst. Steklov. (POMI) 318 (2004), 298-307; English transl., J. Math. Sci. (N.Y.) 136 (2006), no. 2, 3826-3831. · Zbl 1084.47021 |
| [6] | K1 I. Kachkovski\i , Nonexistence of eigenvalues for the periodic Schr\"odinger operator with singular potential in a rectangular cylinder, Funktsional. Anal. i Prilozhen. 47 (2013), no. 2, 27-37; English transl., Funct. Anal. Appl. 47 (2013), no. 2, 104-112. · Zbl 1273.35200 |
| [7] | K2 \bysame , Nonexistence of eigenvalues in the spectrum of some Schr\"odinger operators with periodic coefficients, Kand. Diss., POMI RAN, SPb., 2013. (Russian) |
| [8] | Ku P. Kuchment, Floquet theory for partial differential equations, Oper. Theory Adv. Appl., vol. 60, Birkhauser Verlag, Basel, 1993. · Zbl 0789.35002 |
| [9] | Mo A. Morame, The absolute continuity of the spectrum of Maxwell operator in a periodic media, J. Math. Phys. 41 (2000), no. 10, 7099-7108. · Zbl 1034.82062 |
| [10] | Su T. A. Suslina, Absolute continuity of the spectrum of the periodic Maxwell operator in a layer, Zap. Nauchn. Sem. S.-Peterburg. Mat. Inst. Steklov. (POMI) 288 (2002), 232-255; English transl., J. Math. Sci. (N.Y.) 123 (2004), no. 6, 4654-4667. · Zbl 1068.35081 |
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