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.
Bibliographical noteFunding 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.