A relaxation result for autonomous integral functionals with discontinuous non-coercive integrand

Let L : RN x RN. R be a Borelian function and consider the following problems inf {F(y) = integral(a)(b) L(y(t), y'(t)) dt : y is an element of AC([a,b], R-N), y(a) = A, y(b) = B} (P) inf {F**(y) = integral(a)(b) L**(y(t), y'(t)) dt : y is an element of AC([a,b], R-N), y(a) - A, y(b) = B}, (P**) We give a sufficient condition, weaker then superlinearity, under which inf F = inf F** if L is just continuous in x. We then extend a result of Cellina on the Lipschitz regularity of the minima of ( P) when L is not superlinear.