Null Lagrangians, weak continuity, and variational problems of arbitrary order

J. M. Ball, J. C. Currie, P. J. Olver

Research output: Contribution to journalArticle

Abstract

We consider the problem of minimizing integral functionals of the form I(u) = ?O F(x, ?[k]u(x)) dx, where O ?Rp, 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(?ku) depending only on derivatives of order k. Applications to elasticity and other theories of mechanics are given. © 1981.

Original languageEnglish
Pages (from-to)135-174
Number of pages40
JournalJournal of Functional Analysis
Volume41
Issue number2
Publication statusPublished - Apr 1981

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