Regularity of Solutions to Second-Order Integral Functionals in Variational Calculus
Optimization and Control
2008-02-23 v1
Abstract
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.
Cite
@article{arxiv.0707.2404,
title = {Regularity of Solutions to Second-Order Integral Functionals in Variational Calculus},
author = {Moulay Rchid Sidi Ammi and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:0707.2404},
year = {2008}
}