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

 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_à 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
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}