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

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

Research output: Contribution to journalArticle

171 Citations (Scopus)

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

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Weak Continuity
Variational Problem
Null
Integral Functionals
Arbitrary
Partial derivative
Mechanics
Elasticity
Denote
Derivative
Form

Cite this

Null Lagrangians, weak continuity, and variational problems of arbitrary order. / Ball, J. M.; Currie, J. C.; Olver, P. J.

In: Journal of Functional Analysis, Vol. 41, No. 2, 04.1981, p. 135-174.

Research output: Contribution to journalArticle

Ball, J. M. ; Currie, J. C. ; Olver, P. J. / Null Lagrangians, weak continuity, and variational problems of arbitrary order. In: Journal of Functional Analysis. 1981 ; Vol. 41, No. 2. pp. 135-174.
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