RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
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


Mat. Zametki, 2001, Volume 70, Issue 3, Pages 403–418 (Mi mz752)  

This article is cited in 15 scientific papers (total in 15 papers)

The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral

H. Matevossian

M. V. Lomonosov Moscow State University

Abstract: We study the unique solvability of the Dirichlet problem for the biharmonic equation in the exterior of a compact set under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight $|x|^a$. Depending on the value of the parameter $a$, we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Dirichlet problem.

DOI: https://doi.org/10.4213/mzm752

Full text: PDF file (223 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2001, 70:3, 363–377

Bibliographic databases:

UDC: 517.95
Received: 10.01.2000

Citation: H. Matevossian, “The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral”, Mat. Zametki, 70:3 (2001), 403–418; Math. Notes, 70:3 (2001), 363–377

Citation in format AMSBIB
\Bibitem{Mat01}
\by H.~Matevossian
\paper The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral
\jour Mat. Zametki
\yr 2001
\vol 70
\issue 3
\pages 403--418
\mathnet{http://mi.mathnet.ru/mz752}
\crossref{https://doi.org/10.4213/mzm752}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1882250}
\zmath{https://zbmath.org/?q=an:1049.31008}
\elib{http://elibrary.ru/item.asp?id=13385906}
\transl
\jour Math. Notes
\yr 2001
\vol 70
\issue 3
\pages 363--377
\crossref{https://doi.org/10.1023/A:1012347929056}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000172164200008}


Linking options:
  • http://mi.mathnet.ru/eng/mz752
  • https://doi.org/10.4213/mzm752
  • http://mi.mathnet.ru/eng/mz/v70/i3/p403

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. H. Matevossian, “On solutions of mixed boundary-value problems for the elasticity system in unbounded domains”, Izv. Math., 67:5 (2003), 895–929  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. H. Matevossian, “A uniqueness criterion for solutions of the Robin problem for a system in elasticity theory in exterior domains”, Russian Math. Surveys, 58:2 (2003), 384–385  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. O. A. Matevosyan, “Solutions of the Robin problem for the system of elastic theory in external domains”, J. Math. Sci. (N. Y.), 197:3 (2014), 367–394  mathnet  crossref  elib
    4. Matevosyan O.A., “On Solutions of a Boundary Value Problem For a Polyharmonic Equation in Unbounded Domains”, Russ. J. Math. Phys., 21:1 (2014), 130–132  crossref  mathscinet  zmath  isi  scopus  scopus
    5. S. F. Chichoyan, “Smoothness of Solutions of the Dirichlet Problem for the Biharmonic Equation in Nonsmooth 2D Domains”, Math. Notes, 98:6 (2015), 999–1001  mathnet  crossref  crossref  mathscinet  isi  elib
    6. H. A. Matevossian, “On Solutions of the Neumann Problem for the Biharmonic Equation in Unbounded Domains”, Math. Notes, 98:6 (2015), 990–994  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Matevosyan O.A., “Solution of a Mixed Boundary Value Problem For the Biharmonic Equation With Finite Weighted Dirichlet Integral”, Differ. Equ., 51:4 (2015), 487–501  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Matevosyan O.A., “On solutions of a boundary value problem for the biharmonic equation”, Differ. Equ., 52:10 (2016), 1379–1383  crossref  mathscinet  zmath  isi  elib  scopus
    9. Chichoyan S.F., “Smoothness of solutions of the Dirichlet problem for the biharmonic equation in nonsmooth 2D domains”, Differ. Equ., 52:2 (2016), 260–264  crossref  mathscinet  zmath  isi  elib  scopus
    10. Matevosyan O.A., “On solutions of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains”, Russ. J. Math. Phys., 23:1 (2016), 135–138  crossref  mathscinet  zmath  isi  elib  scopus
    11. H. A. Matevossian, “Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces”, J. Math. Sci. (N. Y.), 234:4 (2018), 440–454  mathnet  crossref
    12. Matevossian H.A., “On the biharmonic Steklov problem in weighted spaces”, Russ. J. Math. Phys., 24:1 (2017), 134–138  crossref  mathscinet  zmath  isi  scopus
    13. Matevossian H.A., “On Solutions of the Mixed Dirichlet-Steklov Problem For the Biharmonic Equation in Exterior Domains”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 151–157  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Matevossian H.A., “On the Steklov-Type Biharmonic Problem in Unbounded Domains”, Russ. J. Math. Phys., 25:2 (2018), 271–276  crossref  mathscinet  isi  scopus  scopus
    15. Matevossian H.A., “On the Polyharmonic Neumann Problem in Weighted Spaces”, Complex Var. Elliptic Equ., 64:1 (2019), 1–7  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:509
    Full text:135
    References:31
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019