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

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

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

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

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

229 Citations (Scopus)

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(?^ku) depending only on derivatives of order k. Applications to elasticity and other theories of mechanics are given. © 1981.

Original language	English
Pages (from-to)	135-174
Number of pages	40
Journal	Journal of Functional Analysis
Volume	41
Issue number	2
Publication status	Published - Apr 1981

Cite this

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title = "Null Lagrangians, weak continuity, and variational problems of arbitrary order",

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. {\textcopyright} 1981.",

author = "Ball, {J. M.} and Currie, {J. C.} and Olver, {P. J.}",

year = "1981",

month = apr,

language = "English",

volume = "41",

pages = "135--174",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "2",

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TY - JOUR

T1 - Null Lagrangians, weak continuity, and variational problems of arbitrary order

AU - Ball, J. M.

AU - Currie, J. C.

AU - Olver, P. J.

PY - 1981/4

Y1 - 1981/4

N2 - 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.

AB - 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.

M3 - Article

SN - 0022-1236

VL - 41

SP - 135

EP - 174

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

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

Abstract

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