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

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

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Abstract

We consider the problem of minimizing integral functionals of the form I(u) = ∝Ω F(x, ▽[k]u(x)) dx, where Ω ⊂Rp, u:ω →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.

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

Bibliographical note

Funding Information:
The research of J.M.B. was partially supported by U.S. Army Contract DAAG20-79-C 0086, that of J.C.C. by a United Kingdom S.R.C. research studentship, and that of P.J.O. by a United Kingdom S.R.C. research grant.

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