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, 1971, Volume 13, Issue 2, Pages 155–185
DOI: https://doi.org/10.1070/SM1971v013n02ABEH001033
(Mi sm3054)
 

This article is cited in 86 scientific papers (total in 86 papers)

On a class of elliptic pseudodifferential operators degenerate on a submanifold

V. V. Grushin
References:
Abstract: There are investigated elliptic pseudodifferential operators $p(x,D)$ which are degenerate on a submanifold $\Gamma$ of any codimension. Under certain further assumptions, for the operator which is obtained by adjoining to $p(x,D)$ boundary and coboundary conditions on the submanifold $\Gamma$, there are constructed left and right regularizers, and theorems on hypoellipticity and local solvability are proved. In case $p(x,D)$ is defined on a smooth compact manifold it is shown to be noetherian on special weighted spaces of Sobolev type.
Bibliography: 24 titles.
Received: 28.04.1970
Bibliographic databases:
UDC: 517.944
MSC: Primary 35S15, 47G05, 58G15; Secondary 35H05
Language: English
Original paper language: Russian
Citation: V. V. Grushin, “On a class of elliptic pseudodifferential operators degenerate on a submanifold”, Math. USSR-Sb., 13:2 (1971), 155–185
Citation in format AMSBIB
\Bibitem{Gru71}
\by V.~V.~Grushin
\paper On a~class of elliptic pseudodifferential operators degenerate on a~submani\-fold
\jour Math. USSR-Sb.
\yr 1971
\vol 13
\issue 2
\pages 155--185
\mathnet{http://mi.mathnet.ru//eng/sm3054}
\crossref{https://doi.org/10.1070/SM1971v013n02ABEH001033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=283630}
\zmath{https://zbmath.org/?q=an:0215.49203|0238.47038}
Linking options:
  • https://www.mathnet.ru/eng/sm3054
  • https://doi.org/10.1070/SM1971v013n02ABEH001033
  • https://www.mathnet.ru/eng/sm/v126/i2/p163
  • This publication is cited in the following 86 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