On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians

Abstract: We prove that the optimal solutions of a calculus of variations problem are Lipschitz continuous. The result is obtained without assuming that the domain of the Lagrangian is the whole space as usually stated in the literature. So, the contribution of this Note is in giving a new sufficient condition for the nonexistence of a Lavrentiev phenomenon. To cite this article: M. Quincampoix, N. Zlateva, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]