Gaps in the Spectrum of the Maxwell Operator with Periodic Coefficients

Communications in Mathematical Physics

Volumn 240, Issue 1-2, 2003, Pages 161-170

  Filonov, N ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242641576     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0904-7     Document Type: Article

References (12)

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2. 2-theory of the Maxwell operator in arbitrary domains. Russ. Math. Surv. 42(6), 75-96 (1987)
3. Birman, M., Solomyak, M.: Weyl asymptotics of the spectrum of the Maxwell operator for domain with a Lipschitz boundary. Vestnik Leningrad. Univ. Math. 20(3), 15-21 (1987)
4. Figotin, A., Kuchment, P.: Band-gap structure of spectra of periodic dielectric and acoustic media. I. Scalar model. SIAM J. Appl. Math. 56, 68-88 (1996); II. Two-dimensional photonic crystals. SIAM J. Appl. Math. 56, 1561-1620 (1996)
5. Figotin, A., Kuchment, P.: Band-gap structure of spectra of periodic dielectric and acoustic media. I. Scalar model. SIAM J. Appl. Math. 56, 68-88 (1996); II. Two-dimensional photonic crystals. SIAM J. Appl. Math. 56, 1561-1620 (1996)
6. Friedlander, L.: On the density of states of periodic media in the large coupling limit. Comm. Partial Diff. Eqs. 27, 355-380 (2002)
7. Hempel, R., Lienau, K.: Spectral properties of the periodic media in large coupling limit. Comm. Partial. Diff. Eqs. 25, 1445-1470 (2000)
8. Kuchment, P.: The mathematics of photonic crystals. In: Mathematical Modeling in Optical Science, Frontiers in Applied Mathematics 22, Philadelphia, PA: SIAM, 2001, Chap. 7, pp. 207-272
9. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. I, New York: Academic Press, 1978
10. Suslina, T.: Absolute continuity of the spectrum of the periodic Maxwell operator in a layer. Zap. Nauch. Sem. POMI (Russian) 288, 232-255 (2002), English translation to appear
11. Suslina, T.: Absolute continuity of the spectrum of periodic operators of mathematical physics. Journées Equations aux dérivées partielles. Nantes, 5-9 juin 2000
12. Weck, N.: Maxwell's boundary value problem on Riemannian manifolds with nonsmooth boundaries. J. Math. Anal. Appl. 46(2), 410-437 (1974)