Lipschitz regularity of the minimizers of autonomous integral functionals with discontinuous non-convex integrands of slow growth

Let L(x, ):RN RN R be a Borelian function and let (P) be the problem of minimizing b a L(y(t), y (t)) dt among the absolutely continuous functions with prescribed values at a and b. We give some sufcient conditions that weaken the classical superlinear growth assumption to ensure that the minima of (P) are Lipschitz. We do not assume convexity of L w.r. to or continuity of L. [PUBLICATION ABSTRACT]