The structure of null Lagrangians

Abstract

We say that L ( x , U , Vu) is a null Lagrangian if and only if the corresponding integral functional g(u) = Jn L(x, U , Vu) dx has the property that g(uIn the homogeneous case, corresponding to L(x, U, Vu) = @(Vu), it is known that a necessary and sufficient condition for L to be a null Lagrangian is that @(Vu) is an affine combination of subdeterminants of Vu of all orders. In this paper we show that all inhomogeneous null Lagrangians may be constructed from these homogeneous ones by introducing appropriate potentials.

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Equivalent and separable strain-energy functions in compressible, finite elasticity

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