Regularity of Solutions to Second-Order Integral Functionals in Variational Calculus

Moulay Rchid Sidi Ammi, Delfim F. M. Torres

Published 2007-07-16Version 1

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 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.