Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. Anâ€¦ (More)

â€“ Under general growth assumptions, that include some cases of linear g we prove existence of Lipschitzian solutions to the problem of minimizing âˆ« b a L(x(s), x â€²(s))ds with the boundary conditionsâ€¦ (More)

We consider a variational problem, where the Lagrangean is of the form f(âˆ‡u)+Î±u. We introduce an explicit family of solutions to this problem and we prove uniqueness and comparison results. We showâ€¦ (More)

We prove existence of solutions to upper semicontinuous differential inclusions and to time optimal control problems under conditions that are strictly weaker than the usual assumption of convexity.

The aim of this paper is to discuss the assumption of strict convexity in problems of the the Calculus of Variations, and to present some results that avoid introducing this assumption. Mathematicsâ€¦ (More)

Under some regularity assumptions on the boundary datum u (assumptions automatically satisfied in the classical case when the growth of the integrand is bounded by a + bâ€–Î¾â€–), we prove the validity ofâ€¦ (More)