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Algebra i Analiz, 2022, Volume 34, Issue 4, Pages 74–106 (Mi aa1825)  

This article is cited in 6 scientific papers (total in 6 papers)

Research Papers

Improved L2L2-approximation of resolvents in homogenization of fourth order operators

S. E. Pastukhova

MIREA — Russian Technological University
References:
Abstract: A 4th order elliptic operator AεAε in the diverdence form acting in the entire space Rd and having ε-periodic coefficients is studied (ε is a small parameter). An approximation for the resolvent (Aε+1)1 is found with error estimate of order ε3 in the operator (L2L2)-norm. The method of double-scale approximation with a generalised shift in the form of smoothing is used.
Keywords: homogenization, error estimates, approximation of the resolvent, elliptic operator of the 4th order.
Received: 08.03.2021
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 4, Pages 611–634
DOI: https://doi.org/10.1090/spmj/1772
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. E. Pastukhova, “Improved L2-approximation of resolvents in homogenization of fourth order operators”, Algebra i Analiz, 34:4 (2022), 74–106; St. Petersburg Math. J., 34:4 (2023), 611–634
Citation in format AMSBIB
\Bibitem{Pas22}
\by S.~E.~Pastukhova
\paper Improved $L^2$-approximation of resolvents in homogenization of fourth order operators
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 4
\pages 74--106
\mathnet{http://mi.mathnet.ru/aa1825}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=548437}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 4
\pages 611--634
\crossref{https://doi.org/10.1090/spmj/1772}
Linking options:
  • https://www.mathnet.ru/eng/aa1825
  • https://www.mathnet.ru/eng/aa/v34/i4/p74
  • This publication is cited in the following 6 articles:
    1. S. E. Pastukhova, “L2-otsenki pogreshnosti usredneniya parabolicheskikh uravnenii s uchetom korrektorov”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 134–151  mathnet  crossref
    2. 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
    3. 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
    4. 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
    5. 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
    6. S. E. Pastukhova, “Improved resolvent approximations in homogenization of second order operators with periodic coefficients”, Funct. Anal. Appl., 56:4 (2022), 310–319  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Алгебра и анализ St. Petersburg Mathematical Journal
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