### 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