2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165171We 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 regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives with respect to the higher-order derivatives admit only minimizers with essentially bounded derivatives.Optimization and Control49N60; 49J30; 49K05text