Mathematics of the USSR-Sbornik
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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mathematics of the USSR-Sbornik, 1987, Volume 57, Issue 2, Pages 591–599
DOI: https://doi.org/10.1070/SM1987v057n02ABEH003088
(Mi sm1846)
 

On approximation of superharmonic functions in open sets

M. Shirinbekov
References:
Abstract: This article deals with an investigation and some applications of the following problem. Let $D\subset\mathbf R^n$, $n\geqslant2$, be a bounded region coinciding with the interior of its closure, let $S(\overline D)$ be the set of bounded superharmonic functions on $D$, and let $S_C^0(\overline D)$ be the set of functions continuous and superharmonic in a neighborhood of $\overline D$. It is necessary to find conditions under which each function $V(x)$ in some subset $S'\subset S(D)$ is representable in the form
$$ V(x)=\varliminf_{y\to x}\inf F(y),\qquad x,y\in D, $$
where the infimum is over a system of functions in $S_C^0(D)$ such that $F(x)>\overline V(x)=\varlimsup_{y\to x}V(y)$, $x,y\in D$. A solution is presented for certain cases when the set $S'$ is specified concretely.
Bibliography: 9 titles.
Received: 26.11.1984
Bibliographic databases:
UDC: 517.5
MSC: Primary 31B05; Secondary 31B15, 32F15
Language: English
Original paper language: Russian
Citation: M. Shirinbekov, “On approximation of superharmonic functions in open sets”, Math. USSR-Sb., 57:2 (1987), 591–599
Citation in format AMSBIB
\Bibitem{Shi86}
\by M.~Shirinbekov
\paper On approximation of superharmonic functions in open sets
\jour Math. USSR-Sb.
\yr 1987
\vol 57
\issue 2
\pages 591--599
\mathnet{http://mi.mathnet.ru//eng/sm1846}
\crossref{https://doi.org/10.1070/SM1987v057n02ABEH003088}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=842401}
\zmath{https://zbmath.org/?q=an:0623.31007}
Linking options:
  • https://www.mathnet.ru/eng/sm1846
  • https://doi.org/10.1070/SM1987v057n02ABEH003088
  • https://www.mathnet.ru/eng/sm/v171/i4/p578
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024