## Advances in Differential Equations

### Extended Hardy-Littlewood inequalities and applications to the calculus of variations

#### Abstract

An extension of the Hardy-Littlewood inequality for rearrangements is established. It is used for giving several conditions of existence of a minimum for nonweakly-lower-semicontinuous functionals of the form $J(v) \! = \! \int_0^1f(x,v(x),v'(x)) dx$ with constraints on $v$ and $v'$.

#### Article information

Source
Adv. Differential Equations Volume 5, Number 7-9 (2000), 1091-1138.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651295

Mathematical Reviews number (MathSciNet)
MR1776349

Zentralblatt MATH identifier
1004.49009

#### Citation

Cardaliaguet, Pierre; Tahraoui, Rabah. Extended Hardy-Littlewood inequalities and applications to the calculus of variations. Adv. Differential Equations 5 (2000), no. 7-9, 1091--1138.https://projecteuclid.org/euclid.ade/1356651295