Abstract
In this Note, we generalize Hardy-Littlewood inequality for integrands of the form ƒ(¦x¦, u), where u is a N-dimensional vector function. We use the result for proving the existence of a minimizer for functionals of the form ∝ 0 1 ƒ(x,v(x),v′(x)) dx under global or pointwise constraints.
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