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Journal of Convex Analysis 10 (2003), No. 2, 477--489
Copyright Heldermann Verlag 2003

On the Relaxation on BV of Certain Non Coercive Integral Functionals

Francesco Maggi
Dip. di Matematica, UniversitÓ di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy,

We prove an integral representation formula for the relaxed functional of a scalar non parametric integral of the Calculus of Variations. Similar results are known to be true under the key assumption that the integrand is coercive in the gradient variable. Here we show that the same integral representation holds for a wide class of non coercive integrands, including for example the strictly convex ones.

Keywords: relaxation, calculus of variations, demicoercivity.

MSC 2000: 49J45.

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