Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matematicheskie Zametki, 2024, Volume 116, Issue 2, Pages 163–184
DOI: https://doi.org/10.4213/mzm14039
(Mi mzm14039)
 

On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with rapidly oscillating boundary

D. I. Borisov, R. R. Suleimanov

Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
References:
Abstract: The paper considers a second-order elliptic operator with variable sufficiently smooth coefficients in an arbitrary two-dimensional domain with rapidly oscillating boundary under the assumption that the oscillation amplitude is small. The structure of the oscillations is fairly arbitrary in that no periodicity or local periodicity conditions are imposed. The oscillating boundary is divided into two components with the Dirichlet boundary condition posed on one of the components and the Neumann condition, on the other. Such mixed boundary conditions are preserved under homogenization; as a result, the functions in the domain of the homogenized operator have weak power-law singularities. Despite these singularities, we have been able to modify the technique in our previous papers appropriately so as to prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and estimate the convergence rate.
Keywords: oscillating boundary, operator estimate, mixed boundary conditions.
Funding agency Grant number
Russian Science Foundation 23-11-00009
The work of the second author was financially supported by the Russian Science Foundation, grant no. 23-11-00009, https://rscf.ru/en/project/23-11-00009/.
Received: 23.05.2023
Revised: 23.02.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 2, Pages 182–199
DOI: https://doi.org/10.1134/S0001434624070149
Document Type: Article
UDC: 517.956
MSC: 35B40, 35J15
Language: Russian
Citation: D. I. Borisov, R. R. Suleimanov, “On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with rapidly oscillating boundary”, Mat. Zametki, 116:2 (2024), 163–184; Math. Notes, 116:2 (2024), 182–199
Citation in format AMSBIB
\Bibitem{BorSul24}
\by D.~I.~Borisov, R.~R.~Suleimanov
\paper On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with rapidly oscillating boundary
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 2
\pages 163--184
\mathnet{http://mi.mathnet.ru/mzm14039}
\crossref{https://doi.org/10.4213/mzm14039}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 2
\pages 182--199
\crossref{https://doi.org/10.1134/S0001434624070149}
Linking options:
  • https://www.mathnet.ru/eng/mzm14039
  • https://doi.org/10.4213/mzm14039
  • https://www.mathnet.ru/eng/mzm/v116/i2/p163
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:93
    Full-text PDF :1
    Russian version HTML:5
    References:19
    First page:10
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024