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

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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 118, Number 3, Pages 347–353
DOI: https://doi.org/10.4213/tmf706 (Mi tmf706)

This article is cited in 22 scientific papers (total in 22 papers)

On the spectrum of the Laplacian with frequently alternating boundary conditions

D. I. Borisov^a, R. R. Gadyl'shin^b

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

Full-text PDF (173 kB) Citations (22)

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

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.

English version:
Theoretical and Mathematical Physics, 1999, Volume 118, Issue 3, Pages 272–277
DOI: https://doi.org/10.1007/BF02557321

Bibliographic databases:

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/tmf706

https://doi.org/10.4213/tmf706

https://www.mathnet.ru/eng/tmf/v118/i3/p347

This publication is cited in the following 22 articles:

D. I. Borisov, “Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions”, J Math Sci, 277:6 (2023), 841
D. I. Borisov, “Asimptoticheskii analiz kraevykh zadach dlya operatora Laplasa s chastoi smenoi tipa granichnykh uslovii”, Differentsialnye uravneniya s chastnymi proizvodnymi, SMFN, 67, no. 1, Rossiiskii universitet druzhby narodov, M., 2021, 14–129
Vorobiev A.M., “Resonance Asymptotics For Quantum Waveguides With Semitransparent Multi-Perforated Wall”, Nanosyst.-Phys. Chem. Math., 12:4 (2021), 462–471
Vorobiev A.M., Trifanova E.S., Popov I.Y., “Resonance Asymptotics For a Pair Quantum Waveguides With Common Semitransparent Perforated Wall”, Nanosyst.-Phys. Chem. Math., 11:6 (2020), 619–627
Vorobiev A.M., Bagmutov A.S., Popov I A., “On Formal Asymptotic Expansion of Resonance For Quantum Waveguide With Perforated Semitransparent Barrier”, Nanosyst.-Phys. Chem. Math., 10:4 (2019), 415–419
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
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
R. I. Bihun, Z. V. Stasyuk, “Impact of Surface Inhomogeneities on Conditions for Charge Transfer in Ultrathin Films of Metals”, Metallofiz. Noveishie Tekhnol., 36:6 (2016), 723
D. I. Borisov, T. F. Sharapov, “On the Resolvent of Multidimensional Operators with Frequently Alternating Boundary Conditions with the Robin Homogenized Condition”, J Math Sci, 213:4 (2016), 461
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
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
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
Chechkina A.G., “On Singular Perturbations of a Steklov-Type Problem with Asymptotically Degenerate Spectrum”, Doklady Mathematics, 84:2 (2011), 695–698
Olendski O., Mikhailovska L., “Theory of a curved planar waveguide with Robin boundary conditions”, Physical Review E, 81:3 (2010), 036606
A. G. Chechkina, “Convergence of solutions and eigenelements of Steklov type boundary value problems with boundary conditions of rapidly varying type”, J Math Sci, 162:3 (2009), 443
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
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
Chechkin, GA, “Non-periodic boundary homogenization and “light” concentrated masses”, Indiana University Mathematics Journal, 54:2 (2005), 321
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
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

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

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