D. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Mat. Zametki, 70:4 (2001), 520–534; Math. Notes, 70:4 (2001), 471

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Matematicheskie Zametki, 2001, Volume 70, Issue 4, Pages 520–534
DOI: https://doi.org/10.4213/mzm764 (Mi mzm764)

This article is cited in 16 scientific papers (total in 16 papers)

Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian

D. I. Borisov

Bashkir State Pedagogical University

Full-text PDF (247 kB) Citations (16)

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DOI: https://doi.org/10.4213/mzm764

Abstract: We study a model boundary-value problem for the Laplacian in the unit disk with closely-spaced and periodic alternation of the type of boundary condition for the case in which the Dirichlet problem is the limit one. We study and justify the two-parameter asymptotics of an eigenvalue of the perturbed problem converging to a simple eigenvalue of the limit problem.

Received: 20.04.1999
Revised: 10.04.2001

English version:
Mathematical Notes, 2001, Volume 70, Issue 4, Pages 471–485
DOI: https://doi.org/10.1023/A:1012372501740

Bibliographic databases:

UDC: 517.956

Language: Russian

Citation: D. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Mat. Zametki, 70:4 (2001), 520–534; Math. Notes, 70:4 (2001), 471–485

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm764

https://doi.org/10.4213/mzm764

https://www.mathnet.ru/eng/mzm/v70/i4/p520

This publication is cited in the following 16 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
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
T. F. Sharapov, “On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition”, Sb. Math., 205:10 (2014), 1492–1527
Denis Borisov, Renata Bunoiu, Giuseppe Cardone, “Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics”, Z. Angew. Math. Phys., 64:3 (2013), 439
Postnikova E.Yu., “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 26, 49–58
E. Yu. Postnikova, “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik ChelGU, 2011, no. 13, 49–58
Borisov, D, “Homogenization of the planar waveguide with frequently alternating boundary conditions”, Journal of Physics A-Mathematical and Theoretical, 42:36 (2009), 365205
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
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 G.A., Koroleva Yu.O., Persson L.-E., “On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure”, J. Inequal. Appl., 2007, 34138
G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, “On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure”, J. Inequal. Appl., 2007 (2007), 1
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
D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008
Borisov, DI, “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady Mathematics, 65:2 (2002), 224

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

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