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TMF, 1999, Volume 118, Number 3, Pages 347–353 (Mi tmf706)  

This article is cited in 14 scientific papers (total in 14 papers)

On the spectrum of the Laplacian with frequently alternating boundary conditions

D. I. Borisova, R. R. Gadyl'shinb

a Bashkir State Pedagogical University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We consider a boundary problem for the Laplacian in a two-dimensional domain with frequently alternating boundary conditions. The leading terms of the asymptotic expansions of the eigenvalues and the corresponding eigenfunctions are constructed under the assumption that the limiting case is the mixed boundary problem.

DOI: https://doi.org/10.4213/tmf706

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English version:
Theoretical and Mathematical Physics, 1999, 118:3, 272–277

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Citation: D. I. Borisov, R. R. Gadyl'shin, “On the spectrum of the Laplacian with frequently alternating boundary conditions”, TMF, 118:3 (1999), 347–353; Theoret. and Math. Phys., 118:3 (1999), 272–277

Citation in format AMSBIB
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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. D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Borisov, DI, “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady Mathematics, 65:2 (2002), 224  mathscinet  zmath  isi
    3. D. I. Borisov, “Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions”, Izv. Math., 67:6 (2003), 1101–1148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. I. Borisov, “Asymptotics and estimates of the convergence rate in a three-dimensional boundary-value problem with rapidly alternating boundary conditions”, Siberian Math. J., 45:2 (2004), 222–240  mathnet  crossref  mathscinet  zmath  isi  elib
    5. Chechkin, GA, “Non-periodic boundary homogenization and “light” concentrated masses”, Indiana University Mathematics Journal, 54:2 (2005), 321  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Perez, E, “On periodic Steklov type eigenvalue problems on half-bands and the spectral homogenization problem”, Discrete and Continuous Dynamical Systems-Series B, 7:4 (2007), 859  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Chechkin, GA, “On boundary-value problems for the Laplacian in bounded domains with micro inhomogeneous structure of the boundaries”, Acta Mathematica Sinica-English Series, 23:2 (2007), 237  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Olendski O., Mikhailovska L., “Theory of a curved planar waveguide with Robin boundary conditions”, Physical Review E, 81:3 (2010), 036606  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    9. V. A. Sadovnichii, A. G. Chechkina, “Ob otsenke sobstvennykh funktsii zadachi tipa Steklova s malym parametrom v sluchae predelnogo vyrozhdeniya spektra”, Ufimsk. matem. zhurn., 3:3 (2011), 127–139  mathnet  zmath
    10. Najar H., Olendski O., “Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs”, J. Phys. A: Math. Theor., 44:30 (2011), 305304  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    11. Chechkina A.G., “On Singular Perturbations of a Steklov-Type Problem with Asymptotically Degenerate Spectrum”, Doklady Mathematics, 84:2 (2011), 695–698  crossref  mathscinet  zmath  isi  elib  elib  scopus
    12. A. G. Chechkina, V. A. Sadovnichy, “Degeneration of Steklov–type boundary conditions in one spectral homogenization problem”, Eurasian Math. J., 6:3 (2015), 13–29  mathnet
    13. Bihun R.I., Stasyuk Z.V., Balitskii O.A., “Crossover From Quantum To Classical Electron Transport in Ultrathin Metal Films”, Physica B, 487 (2016), 73–77  crossref  adsnasa  isi  scopus  scopus  scopus
    14. T. F. Sharapov, “On resolvent of multi-dimensional operators with frequent alternation of boundary conditions: critical case”, Ufa Math. J., 8:2 (2016), 65–94  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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