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



Eurasian Math. J.:
Year:
Volume:
Issue:
Page:
Find






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


Eurasian Math. J., 2016, Volume 7, Number 1, Pages 28–49 (Mi emj214)  

Inequalities between the norms of a function and its derivatives

A. S. Kochurov

Department of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow 119991, Russia

Abstract: The paper is devoted to the problem of finding the maximum of the norm $||x||_q$ with the constraints $||x||_p=\eta$, $||\dot{x}||_r=\sigma$, $x(0)=a$, $a, \sigma, \eta>0$, for functions $x\in L_p(\mathbb{R}_-)$ with derivatives $\dot{x}\in L_r(\mathbb{R_-})$, $0 < p \leqslant q < \infty$, $r > 1$. The arguments employed are based on the standard machinery of the calculus of variations.

Keywords and phrases: inequalities for derivatives, necessary conditions for an extremum, Weierstrass formula, Euler equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00744_
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00744).


Full text: PDF file (440 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 26D10
Received: 30.11.2015
Language:

Citation: A. S. Kochurov, “Inequalities between the norms of a function and its derivatives”, Eurasian Math. J., 7:1 (2016), 28–49

Citation in format AMSBIB
\Bibitem{Koc16}
\by A.~S.~Kochurov
\paper Inequalities between the norms of a function and its derivatives
\jour Eurasian Math. J.
\yr 2016
\vol 7
\issue 1
\pages 28--49
\mathnet{http://mi.mathnet.ru/emj214}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380176800002}


Linking options:
  • http://mi.mathnet.ru/eng/emj214
  • http://mi.mathnet.ru/eng/emj/v7/i1/p28

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Eurasian Mathematical Journal
    Number of views:
    This page:247
    Full text:110
    References:26

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019