Advances in Differential Equations

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

Pierre Cardaliaguet and Rabah Tahraoui

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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

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

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J10: Free problems in two or more independent variables
Secondary: 49J15: Optimal control problems involving ordinary differential equations


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.

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