2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155434We 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 phenomenon. Our main result asserts that autonomous integral functionals of the calculus of variations with a Lagrangian having superlinearity partial derivatives with respect to the higher-order derivatives admit only minimizers with essentially bounded derivatives.Optimization and Control49N60; 49J30; 49K05text