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

摘要

Let L(x, xi) : R-N x R-N -> R be a Borelian function and let (P) be the problem of minimizing integral(b)(a) L(y(t), y'(t)) dt among the absolutely continuous functions with prescribed values at a and b. We give some sufficient 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 xi or continuity of L.