### Abstract

We consider the problem of minimizing integral functionals of the form I(u) = ?_{O} F(x, ?^{[k]}u(x)) dx, where O ?R^{p}, u:? ?R and ?^{[k]}u denotes the set of all partial derivatives of u with orders =k. The method is based on a characterization of null Lagrangians L(?^{k}u) depending only on derivatives of order k. Applications to elasticity and other theories of mechanics are given. © 1981.

Original language | English |
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Pages (from-to) | 135-174 |

Number of pages | 40 |

Journal | Journal of Functional Analysis |

Volume | 41 |

Issue number | 2 |

Publication status | Published - Apr 1981 |

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## Cite this

Ball, J. M., Currie, J. C., & Olver, P. J. (1981). Null Lagrangians, weak continuity, and variational problems of arbitrary order.

*Journal of Functional Analysis*,*41*(2), 135-174.