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

This article is cited in 11 scientific papers (total in 11 papers)

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


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

Bibliographic databases:

UDC: 517.946
Received: 07.05.2007

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
\by S.~A.~Nazarov
\paper The Essential Spectrum of Boundary Value Problems for Systems of Differential Equations in a Bounded Domain with a~Cusp
\jour Funktsional. Anal. i Prilozhen.
\yr 2009
\vol 43
\issue 1
\pages 55--67
\jour Funct. Anal. Appl.
\yr 2009
\vol 43
\issue 1
\pages 44--54

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    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  mathnet  crossref  mathscinet  isi  elib  elib
    2. S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi
    6. A. I. Noarov, “Existence and nonuniqueness of solutions to a functional-differential equation”, Siberian Math. J., 53:6 (2012), 1115–1118  mathnet  crossref  mathscinet  isi  elib  elib
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi
    9. A.I. Noarov, “A system of elliptic equations for probability measures”, Dokl. Math., 90:2 (2014), 529–534  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib
    10. Kozlov V., Nazarov S.A., “on the Spectrum of An Elastic Solid With Cusps”, Adv. Differ. Equat., 21:9-10 (2016), 887–944  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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