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, 1970, Volume 10, Issue 1, Pages 1–19
DOI: https://doi.org/10.1070/SM1970v010n01ABEH002151
(Mi sm3357)
 

This article is cited in 10 scientific papers (total in 10 papers)

On equations of minimax type in the theory of elliptic and parabolic equations in the plane

N. V. Krylov
References:
Abstract: The existence and uniqueness of the solution in Sobolev spaces $W_p^2$ ($W_p^{2,1}$) is proved for the first boundary value problem for elliptic (parabolic) equations of the form
$$ \lambda u-\inf_{\alpha\in\mathfrak U}\sup_{\beta\in\mathfrak B(\alpha)}(L_{\alpha\beta}u+f_{\alpha\beta})=f. $$

Here $L_{\alpha\beta}u=a_{ij}^{\alpha\beta}D_{ij}u+b_i^{\alpha\beta}u_{x_i}-c^{\alpha\beta}u$ and $D_{ij}u=u_{x_ix_j}$ in the elliptic case, $D_{ij}u=u_{x_ix_j}-\delta_{ij}u_t$ in the parabolic case. The subscript $p$ takes any values close to two.
Bibliography: 10 titles.
Received: 08.12.1968
Bibliographic databases:
UDC: 517.944/947
Language: English
Original paper language: Russian
Citation: N. V. Krylov, “On equations of minimax type in the theory of elliptic and parabolic equations in the plane”, Math. USSR-Sb., 10:1 (1970), 1–19
Citation in format AMSBIB
\Bibitem{Kry70}
\by N.~V.~Krylov
\paper On equations of minimax type in the theory of elliptic and parabolic equations in the plane
\jour Math. USSR-Sb.
\yr 1970
\vol 10
\issue 1
\pages 1--19
\mathnet{http://mi.mathnet.ru//eng/sm3357}
\crossref{https://doi.org/10.1070/SM1970v010n01ABEH002151}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=255954}
\zmath{https://zbmath.org/?q=an:0213.11803|0215.16205}
Linking options:
  • https://www.mathnet.ru/eng/sm3357
  • https://doi.org/10.1070/SM1970v010n01ABEH002151
  • https://www.mathnet.ru/eng/sm/v123/i1/p3
  • This publication is cited in the following 10 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