This monograph is devoted to the study of nonconvex optimal control and variational
problems. It contains a number of recent results obtained by the author in the last 15 years …

In this paper we study nonoccurrence of the Lavrentiev phenomenon for a large class of
nonconvex optimal control problems identified with the corresponding complete metric …

Whereas in a coordinate-dependent setting the Euler–Lagrange equations establish
necessary conditions for solving variational problems in which both the integrands of …

The words” Calculus of Variations” were first used by L. Euler in 1760 ([25]) after he had
been astonished by a letter from J. Lagrange, where a new method (based on what we …

The aim of this work is to give a simple proof of the Tonelli's partial regularity result which
states that any absolutely continuous solution to the variational problem $$\min\left\{\int_a^ b …

In this work we prove that, if L (t, u, ξ) is a continuous function in t and u, Borel measurable in
ξ, with bounded non-convex pieces in ξ, then any absolutely continuous solution u¯ to the …

In this work we prove that the symmetries of a Lagrangian function L play an important role
in the regularity of the solutions to its associated variational problem. More precisely, we …

We obtain new regularity conditions for problems of calculus of variations with higher-order
derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main …

In this paper, we study nonoccurrence of the Lavrentiev phenomenon for a large class of
nonconvex optimal control problems. We establish that for most problems (in the sense of …

We obtain regularity conditions of a new type of problems of the calculus of variations with
second-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev …