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, 1990, Volume 65, Issue 1, Pages 229–247
DOI: https://doi.org/10.1070/SM1990v065n01ABEH001930
(Mi sm1784)
 

This article is cited in 22 scientific papers (total in 22 papers)

Selfadjoint extensions of the Dirichlet problem operator in weighted function spaces

S. A. Nazarov
References:
Abstract: The operators considered here are symmetric in $L_2$ with the weight $|x|^{2\sigma}$ and correspond to Dirichlet problems for formally selfadjoint elliptic (in the Petrovskii sense) systems of differential equations of order $2m$ in a bounded domain $\Omega\subset\mathbf R^n$, $O\in\Omega$. All selfadjoint extensions of the operators are listed for every $\sigma\geqslant-m$ with exception of a countable set of half-integer exponents. It is shown that with increasing $\sigma$ the asymptotic conditions at $O$ corresponding to these extensions include all the higher derivatives of the fundamental solution. Analogous assertions concerning the case $O\in\partial\Omega$ are given.
Bibliography: 20 titles.
Received: 12.06.1987
Bibliographic databases:
UDC: 517.946
MSC: Primary 35J40, 35B40; Secondary 47B15, 47A20, 46E35, 47A53, 47A56
Language: English
Original paper language: Russian
Citation: S. A. Nazarov, “Selfadjoint extensions of the Dirichlet problem operator in weighted function spaces”, Math. USSR-Sb., 65:1 (1990), 229–247
Citation in format AMSBIB
\Bibitem{Naz88}
\by S.~A.~Nazarov
\paper Selfadjoint extensions of the Dirichlet problem operator in weighted function spaces
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 1
\pages 229--247
\mathnet{http://mi.mathnet.ru//eng/sm1784}
\crossref{https://doi.org/10.1070/SM1990v065n01ABEH001930}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=971695}
\zmath{https://zbmath.org/?q=an:0683.35033}
Linking options:
  • https://www.mathnet.ru/eng/sm1784
  • https://doi.org/10.1070/SM1990v065n01ABEH001930
  • https://www.mathnet.ru/eng/sm/v179/i2/p224
  • This publication is cited in the following 22 articles:
    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