Nazarov, S. A. Gap in the essential spectrum of the Neumann problem for an elliptic system in a periodic domain. (English. Russian original) Zbl 1271.35025 Funct. Anal. Appl. 43, No. 3, 239-241 (2009); translation from Funkts. Anal. Prilozh. 43, No. 3, 92-95 (2009). Summary: We establish the existence of a gap in the essential spectrum of the Neumann problem for an elliptic formally self-adjoint system of second-order differential equations on a quasi-cylinder (a domain with periodically varying cross-section). Cited in 3 Documents MSC: 35J57 Boundary value problems for second-order elliptic systems 35P05 General topics in linear spectral theory for PDEs Keywords:gap in essential spectrum; Neumann problem for elliptic system; periodic domain; quasi-cylinder PDF BibTeX XML Cite \textit{S. A. Nazarov}, Funct. Anal. Appl. 43, No. 3, 239--241 (2009; Zbl 1271.35025); translation from Funkts. Anal. Prilozh. 43, No. 3, 92--95 (2009) Full Text: DOI References: [1] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Masson-Academia, Paris-Prague, 1967. [2] S. A. Nazarov, Uspekhi Mat. Nauk, 54:5 (1999), 77–142. · doi:10.4213/rm204 [3] M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Selfadjoint Operators in Hilbert Space [in Russian], Leningrad State University, Leningrad, 1980. [4] P. A. Kuchment, Uspekhi Mat. Nauk, 37:4 (1982), 3–52. [5] P. Kuchment, Floquet theory for partial differential equations, Birchäuser, Basel, 1993. · Zbl 0789.35002 [6] S. A. Nazarov and B. A. Plamenevskii, Elliptic Problems in Domains with Piecewise Smooth Boundary [in Russian], Nauka, Moscow, 1991. [7] I. M. Gelfand, Dokl. Akad. Nauk SSSR, 73 (1950), 1117–1120. [8] P. Kuchment, in: Mathematical Modelling in Optical Science, Frontiers in Applied Mathematics, vol. 22, SIAM, Philadelphia, PA, 2001, 207–272. [9] V. V. Zhikov, Algebra and Analiz, 6:5 (2004), 34–58. [10] N. Filonov, Comm. Math. Physics, 6:1–2 (2003), 161–170. · Zbl 1037.35051 · doi:10.1007/s00220-003-0904-7 [11] S. A. Nazarov, Uspekhi Mat. Nauk, 63:5 (2008), 37–110. · doi:10.4213/rm8545 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.