We consider the problem of minimizing integral functionals of the form I(u) = jp F(x, ""'u(x)) dx, where II c IR', u: $2-+ iR4 and V% denotes the set of all partial derivatives of u with orders c/c. 'The method is based on a characterization of null Lagrangians L(V"u) depending only on derivatives of order k. Applications to elasticity and other theories of mechanics are given.
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