The structure of null Lagrangians

P. J. Olver, J. Sivaloganathan

Research output: Contribution to journalArticlepeer-review


It is said that L(x,u, Del u) is a null Lagrangian if and only if the corresponding integral functional E(u)= integral OmegaL(x,u, Del u) dx has the property that E(u+ phi )=E(u) For all phi in C0 infinity( Omega ), for any choice of u in C1( Omega ). In the homogeneous case, corresponding to L(x,u, Del u)= Phi ( Del u), it is known that a necessary and sufficient condition for L to be a null Lagrangian is that Phi ( Del u) is an affine combination of subdeterminants of Del u of all orders. The authors show that all inhomogeneous null Lagrangians may be constructed from these homogeneous ones by introducing appropriate potentials.

Original languageEnglish
Article number005
Pages (from-to)389-398
Number of pages10
Issue number2
Publication statusPublished - 1988

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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