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Mat. Zametki, 1999, Volume 65, Issue 4, Pages 496–510 (Mi mz1076)  

This article is cited in 19 scientific papers (total in 19 papers)

Averaging of operators with a fine-scaled structure of boundary conditions

A. Yu. Belyaeva, G. A. Chechkinb

a Water Problems Institute of the Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

DOI: https://doi.org/10.4213/mzm1076

Full text: PDF file (268 kB)
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English version:
Mathematical Notes, 1999, 65:4, 418–429

Bibliographic databases:

UDC: 517.9
Received: 08.05.1996
Revised: 30.09.1998

Citation: A. Yu. Belyaev, G. A. Chechkin, “Averaging of operators with a fine-scaled structure of boundary conditions”, Mat. Zametki, 65:4 (1999), 496–510; Math. Notes, 65:4 (1999), 418–429

Citation in format AMSBIB
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\pages 496--510
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\transl
\jour Math. Notes
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\pages 418--429
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. Chechkin, GA, “On boundary-value problems for the Laplacian in bounded and in unbounded domains with perforated boundaries”, Journal of Differential Equations, 216:2 (2005), 502  crossref  mathscinet  zmath  isi  scopus  scopus
    5. 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
    6. Chechkin, GA, “Asymptotic analysis of a boundary-value problem in a cascade thick junction with a random transmission zone”, Applicable Analysis, 88:10–11 (2009), 1543  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Chechkin, GA, “HOMOGENIZATION IN DOMAINS RANDOMLY PERFORATED ALONG THE BOUNDARY”, Discrete and Continuous Dynamical Systems-Series B, 12:4 (2009), 713  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Chechkin G.A., Chechkina T.P., D'Apice C., De Maio U., Mel'nyk T.A., “Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction”, Russian Journal of Mathematical Physics, 17:1 (2010), 35–55  crossref  mathscinet  zmath  adsnasa  isi  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. Amirat Y., Bodart O., Chechkin G.A., Piatnitski A.L., “Boundary Homogenization in Domains with Randomly Oscillating Boundary”, Stoch. Process. Their Appl., 121:1 (2011), 1–23  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Moussa A.A., Zlaiji L., “Dimension Reduction and Homogenization of Random Degenerate Operators. Part I”, LMS J. Comput. Math., 15 (2012), 1–22  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. Chechkin G.A., D'Apice C., De Maio U., Piatnitski A.L., “On the Rate of Convergence of Solutions in Domain With Random Multilevel Oscillating Boundary”, Asymptotic Anal., 87:1-2 (2014), 1–28  crossref  mathscinet  zmath  isi  scopus  scopus
    14. A. G. Chechkina, V. A. Sadovnichy, “Degeneration of Steklovtype boundary conditions in one spectral homogenization problem”, Eurasian Math. J., 6:3 (2015), 13–29  mathnet
    15. A. G. Chechkina, “Homogenization of spectral problems with singular perturbation of the Steklov condition”, Izv. Math., 81:1 (2017), 199–236  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. Chechkin G.A., Chechkina T.P., “Asymptotic Behavior of the Spectrum of An Elliptic Problem in a Domain With Aperiodically Distributed Concentrated Masses”, C. R. Mec., 345:10 (2017), 671–677  crossref  isi  scopus  scopus
    17. Chechkina A.G., “Estimate of the Spectrum Deviation of the Singularly Perturbed Steklov Problem”, Dokl. Math., 96:2 (2017), 510–513  crossref  mathscinet  zmath  isi  scopus  scopus
    18. Chechkina A.G., D'Apice C., De Maio U., “Rate of Convergence of Eigenvalues to Singularly Perturbed Steklov-Type Problem For Elasticity System”, Appl. Anal., 98:1-2, SI (2019), 32–44  crossref  mathscinet  isi  scopus
    19. El Jarroudi M., “A Mathematical Model For Turbulent Transport Through Thin Randomly Oscillating Layers Surrounding a Fixed Domain”, Physica A, 520 (2019), 178–195  crossref  mathscinet  isi  scopus
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