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 Funktsional. Anal. i Prilozhen., 2009, Volume 43, Issue 1, Pages 55–67 (Mi faa2934)

The Essential Spectrum of Boundary Value Problems for Systems of Differential Equations in a Bounded Domain with a Cusp

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Peterburg

Abstract: Simple algebraic conditions are found for the existence of essential spectrum of the Neumann problem operator for a formally self-adjoint elliptic system of differential equations in a domain with a cuspidal singular point. The spectrum is discrete in the scalar case.

Keywords: peak, cusp, self-adjoint system of differential equations with the polynomial property; essential, continuous, and discrete spectra

DOI: https://doi.org/10.4213/faa2934

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English version:
Functional Analysis and Its Applications, 2009, 43:1, 44–54

Bibliographic databases:

UDC: 517.946

Citation: S. A. Nazarov, “The Essential Spectrum of Boundary Value Problems for Systems of Differential Equations in a Bounded Domain with a Cusp”, Funktsional. Anal. i Prilozhen., 43:1 (2009), 55–67; Funct. Anal. Appl., 43:1 (2009), 44–54

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/faa2934
• https://doi.org/10.4213/faa2934
• http://mi.mathnet.ru/eng/faa/v43/i1/p55

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. F. L. Bakharev, S. A. Nazarov, “On the structure of the spectrum for the elasticity problem in a body with a supersharp spike”, Siberian Math. J., 50:4 (2009), 587–595
2. S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594
3. Nazarov S.A., Taskinen J., “On essential and continuous spectra of the linearized water-wave problem in a finite pond”, Math. Scand., 106:1 (2010), 141–160
4. Campbell A., Nazarov S.A., Sweers G.H., “Spectra of two-dimensional models for thin plates with sharp edges”, SIAM J. Math. Anal., 42:6 (2010), 3020–3044
5. Nazarov S.A., Taskinen J., “Radiation conditions at the top of a rotational cusp in the theory of water-waves”, ESAIM Math. Model. Numer. Anal., 45:5 (2011), 947–979
6. A. I. Noarov, “Existence and nonuniqueness of solutions to a functional-differential equation”, Siberian Math. J., 53:6 (2012), 1115–1118
7. Kamotski I.V., Maz'ya V.G., “On the linear water wave problem in the presence of a critically submerged body”, SIAM J. Math. Anal., 44:6 (2012), 4222–4249
8. Martin J., “On Continuous Spectrum of the Linearised Water-Wave Problem in Bounded Domains”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 38:2 (2013), 413–431
9. A.I. Noarov, “A system of elliptic equations for probability measures”, Dokl. Math., 90:2 (2014), 529–534
10. Kozlov V., Nazarov S.A., “on the Spectrum of An Elastic Solid With Cusps”, Adv. Differ. Equat., 21:9-10 (2016), 887–944
11. Eismontaite A. Pileckas K., “On Singular Solutions of Time-Periodic and Steady Stokes Problems in a Power Cusp Domain”, Appl. Anal., 97:3 (2018), 415–437
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