Regularity of solutions to higher-order integrals of the calculus of variations

Details Regularity of solutions to higher-order integrals of the calculus of variations Regularity of solutions to higher-order integrals of the calculus of variations

2007-07-18

arxiv.org/abs/0707.2816v1

International Journal of Systems Science, Vol. 39, No. 9, pp. 889--895, 2008

Mathematics

Optimization and Control

Scientific paper

10.1080/00207720802184733

We 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.

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