Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Francesco Maggi

Dip. di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy

maggi@math.unifi.it

Keywords

  • relaxation
  • calculus of variations
  • demicoercivity

Mathematics Subject Classification

49J45

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Suggested citation

F. Maggi. “On the Relaxation on BV of Certain Non Coercive Integral Functionals.” Journal of Convex Analysis 10 (2003), No. 2, 477–489. https://doi.org/10.68381/jca1029

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.