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, 2000, Volume 68, Issue 6, Pages 874–886
DOI: https://doi.org/10.4213/mzm1011 (Mi mzm1011) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Weak Solvability of the Dirichlet Problem on Stratified Sets

O. M. Penkin, E. M. Bogatov

Voronezh State University
Full-text PDF (838 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm1011
Abstract: The Dirichlet problem is posed for an analog of the Beltrami–Laplace operator on sets consisting of manifolds of various dimensions regularly adjacent to one another (stratified sets). A special system of notions permits one to prove analogs of Green's integral identities and the Poincaré inequality for Sobolev type spaces. The weak solvability of the Dirichlet problem for this operator, as well as for an analog of the biharmonic operator, is proved on the basis of the Riesz theorem on the representation of linear functionals.
Received: 02.11.1998
Revised: 01.02.2000
English version:
Mathematical Notes, 2000, Volume 68, Issue 6, Pages 740–750
DOI: https://doi.org/10.1023/A:1026660700355
Bibliographic databases:
UDC: 517.956.2
Language: Russian
Citation: O. M. Penkin, E. M. Bogatov, “Weak Solvability of the Dirichlet Problem on Stratified Sets”, Mat. Zametki, 68:6 (2000), 874–886; Math. Notes, 68:6 (2000), 740–750
Citation in format AMSBIB
\Bibitem{PenBog00}
\by O.~M.~Penkin, E.~M.~Bogatov
\paper Weak Solvability of the Dirichlet Problem on Stratified Sets
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 6
\pages 874--886
\mathnet{http://mi.mathnet.ru/mzm1011}
\crossref{https://doi.org/10.4213/mzm1011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1835187}
\zmath{https://zbmath.org/?q=an:0995.58017}
\elib{https://elibrary.ru/item.asp?id=14024567}
\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 6
\pages 740--750
\crossref{https://doi.org/10.1023/A:1026660700355}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000166684000027}
Linking options:
  • https://www.mathnet.ru/eng/mzm1011
  • https://doi.org/10.4213/mzm1011
  • https://www.mathnet.ru/eng/mzm/v68/i6/p874
    • This publication is cited in the following 6 articles:
    1. S. L. Semenov, “Razreshimost v klassicheskom smysle zadachi Puassona dlya operatora Laplasa na dvumernykh stratifitsirovannykh mnozhestvakh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 12:1 (2012), 38–52  mathnet  crossref  elib
    2. R. Ch. Kulaev, “O funktsii Grina parabolicheskoi zadachi na grafe”, Vladikavk. matem. zhurn., 14:4 (2012), 32–40  mathnet
    3. L. A. Kovaleva, “O modifitsirovannoi zadache Bitsadze–Samarskogo”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(14) (2007), 10–15  mathnet  crossref
    4. E. M. Bogatov, “Approximation of the eigenfrequencies of a triangular grid of bars”, Comput. Math. Math. Phys., 45:8 (2005), 1350–1357  mathnet  mathscinet  zmath
    5. E. M. Bogatov, O. M. Penkin, “The Fourier method in the Cauchy problem for a fourth-order equation on stratified sets”, Russian Math. (Iz. VUZ), 47:8 (2003), 65–69  mathnet  mathscinet  zmath  elib
    6. Bogatov, EM, “On the solvability of hyperbolic equations and elliptic inequalities on stratified sets”, Differential Equations, 39:12 (2003), 1794  mathnet  crossref  mathscinet  zmath  isi  scopus
    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:444
    Full-text PDF :241
    References:73
    First page:1
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025