On the Relaxation on BV of Certain Non Coercive Integral Functionals

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.