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Funktsional'nyi Analiz i ego Prilozheniya, 2020, Volume 54, Issue 3, Pages 94–99
DOI: https://doi.org/10.4213/faa3807
(Mi faa3807)
 

This article is cited in 13 scientific papers (total in 13 papers)

Brief communications

Homogenization of the Fourth-Order Elliptic Operator with Periodic Coefficients with Correctors Taken into Account

V. A. Sloushch, T. A. Suslina

St. Petersburg State University, St. Petersburg, Russia
References:
Abstract: An elliptic fourth-order differential operator Aε on L2(Rd;Cn) is studied. Here ε>0 is a small parameter. It is assumed that the operator is given in the factorized form Aε=b(D)g(x/ε)b(D), where g(x) is a Hermitian matrix-valued function periodic with respect to some lattice and b(D) is a matrix second-order differential operator. We make assumptions ensuring that the operator Aε is strongly elliptic. The following approximation for the resolvent (Aε+I)1 in the operator norm of L2(Rd;Cn) is obtained:
(Aε+I)1=(A0+I)1+εK1+ε2K2(ε)+O(ε3).
Here A0 is the effective operator with constant coefficients and K1 and K2(ε) are certain correctors.
Keywords: periodic differential operators, homogenization, operator error estimates, effective operator, corrector.
Funding agency Grant number
Russian Science Foundation 17-11-01069
This work was supported by the Russian Science Foundation, project no. 17-11-01069.
Received: 07.07.2020
Revised: 09.07.2020
Accepted: 12.07.2020
English version:
Functional Analysis and Its Applications, 2020, Volume 54, Issue 3, Pages 224–228
DOI: https://doi.org/10.1134/S0016266320030077
Bibliographic databases:
Document Type: Article
UDC: 517.956.2
Language: Russian
Citation: V. A. Sloushch, T. A. Suslina, “Homogenization of the Fourth-Order Elliptic Operator with Periodic Coefficients with Correctors Taken into Account”, Funktsional. Anal. i Prilozhen., 54:3 (2020), 94–99; Funct. Anal. Appl., 54:3 (2020), 224–228
Citation in format AMSBIB
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Linking options:
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  • https://doi.org/10.4213/faa3807
  • https://www.mathnet.ru/eng/faa/v54/i3/p94
  • This publication is cited in the following 13 articles:
    1. S. E. Pastukhova, “Improved Homogenization Estimates for Higher-order Elliptic Operators in Energy Norms”, Lobachevskii J Math, 45:7 (2024), 3351  crossref
    2. V. A. Sloushch, T. A. Suslina, “Operator estimates for homogenization of higher-order elliptic operators with periodic coefficients”, St. Petersburg Math. J., 35:2 (2024), 327–375  mathnet  crossref
    3. S. E. Pastukhova, “On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems”, Math. Notes, 114:3 (2023), 322–338  mathnet  crossref  crossref  mathscinet
    4. T. A. Suslina, “Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients”, Russian Math. Surveys, 78:6 (2023), 1023–1154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. A. A. Raev, V. A. Slousch, T. A. Suslina, “Usrednenie odnomernogo periodicheskogo operatora chetvertogo poryadka s singulyarnym potentsialom”, Matematicheskie voprosy teorii rasprostraneniya voln. 53, Zap. nauchn. sem. POMI, 521, POMI, SPb., 2023, 212–239  mathnet
    6. A. A. Miloslova, T. A. Suslina, “Homogenization of the higher-order parabolic equations with periodic coefficients”, J. Math. Sci., 277:6 (2023), 959  crossref  mathscinet
    7. A. Piatnitski, V. Sloushch, T. Suslina, E. Zhizhina, “On operator estimates in homogenization of nonlocal operators of convolution type”, Journal of Differential Equations, 352 (2023), 153  crossref
    8. S. E. Pastukhova, “Improved L2-approximation of resolvents in homogenization of fourth order operators”, St. Petersburg Math. J., 34:4 (2023), 611–634  mathnet  crossref  mathscinet
    9. S. E. Pastukhova, “Approximation of resolvents in homogenization of fourth-order elliptic operators”, Sb. Math., 212:1 (2021), 111–134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. V. A. Sloushch, T. A. Suslina, “Threshold approximations for the resolvent of a polynomial nonnegative operator pencil”, St. Petersburg Math. J., 33:2 (2022), 355–385  mathnet  crossref
    11. A. A. Miloslova, T. A. Suslina, “Usrednenie parabolicheskikh uravnenii vysokogo poryadka s periodicheskimi koeffitsientami”, Differentsialnye uravneniya s chastnymi proizvodnymi, SMFN, 67, no. 1, Rossiiskii universitet druzhby narodov, M., 2021, 130–191  mathnet  crossref
    12. T. A. Suslina, “Homogenization of the Higher-Order Hyperbolic Equations with Periodic Coefficients”, Lobachevskii J Math, 42:14 (2021), 3518  crossref  mathscinet
    13. S. E. Pastukhova, “L2- Approximation of Resolvents in Homogenization of Higher Order Elliptic Operators”, J Math Sci, 251:6 (2020), 902  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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