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

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

Bibliographic databases:

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
\Bibitem{BorGad99} \by D.~I.~Borisov, R.~R.~Gadyl'shin \paper On the spectrum of the Laplacian with frequently alternating boundary conditions \jour TMF \yr 1999 \vol 118 \issue 3 \pages 347--353 \mathnet{http://mi.mathnet.ru/tmf706} \crossref{https://doi.org/10.4213/tmf706} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1713724} \zmath{https://zbmath.org/?q=an:0945.35066} \elib{http://elibrary.ru/item.asp?id=13331139} \transl \jour Theoret. and Math. Phys. \yr 1999 \vol 118 \issue 3 \pages 272--277 \crossref{https://doi.org/10.1007/BF02557321} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000080492800004} 

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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
2. Borisov, DI, “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady Mathematics, 65:2 (2002), 224
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
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
5. Chechkin, GA, “Non-periodic boundary homogenization and “light” concentrated masses”, Indiana University Mathematics Journal, 54:2 (2005), 321
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
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
8. Olendski O., Mikhailovska L., “Theory of a curved planar waveguide with Robin boundary conditions”, Physical Review E, 81:3 (2010), 036606
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
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
11. Chechkina A.G., “On Singular Perturbations of a Steklov-Type Problem with Asymptotically Degenerate Spectrum”, Doklady Mathematics, 84:2 (2011), 695–698
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
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
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
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