Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




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

Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 4, Pages 789–810 (Mi smj1745)  
This article is cited in 5 scientific papers (total in 5 papers)

Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function

M. V. Korobkova, E. Yu. Panovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novgorod State University after Yaroslav the Wise
Full-text PDF (497 kB) Citations (5)
References:
PDF
HTML
Abstract: We find some necessary and sufficient conditions for a plane curve to be the gradient range of a $C^1$-smooth function of two variables. As one of the consequences we give the necessary and sufficient conditions on a continuous function $\varphi$ under which the differential equation $\dfrac{\partial v}{\partial t}=\varphi\biggl(\dfrac{\partial v}{\partial x}\biggr)$ has nontrivial $C^1$-smooth solutions.
Keywords: $C^1$-smooth function, gradient range, curve.
Received: 25.01.2006
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 4, Pages 629–647
DOI: https://doi.org/10.1007/s11202-007-0065-6
Bibliographic databases:
Language: Russian
Citation: M. V. Korobkov, E. Yu. Panov, “Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function”, Sibirsk. Mat. Zh., 48:4 (2007), 789–810; Siberian Math. J., 48:4 (2007), 629–647
Citation in format AMSBIB
\Bibitem{KorPan07}
\by M.~V.~Korobkov, E.~Yu.~Panov
\paper Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 4
\pages 789--810
\mathnet{http://mi.mathnet.ru/smj1745}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2355374}
\zmath{https://zbmath.org/?q=an:1164.26326}
\elib{https://elibrary.ru/item.asp?id=9516494}
\transl
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 4
\pages 629--647
\crossref{https://doi.org/10.1007/s11202-007-0065-6}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000249307000006}
\elib{https://elibrary.ru/item.asp?id=13551059}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548089361}
Linking options:
  • https://www.mathnet.ru/eng/smj1745
  • https://www.mathnet.ru/eng/smj/v48/i4/p789
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024