TY - JOUR
T1 - The structure of null Lagrangians
AU - Olver, Peter J
AU - Sivaloganathan, J.
PY - 1988/12/1
Y1 - 1988/12/1
N2 - 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.
AB - 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.
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U2 - 10.1088/0951-7715/1/2/005
DO - 10.1088/0951-7715/1/2/005
M3 - Article
AN - SCOPUS:6344244957
SN - 0951-7715
VL - 1
SP - 389
EP - 398
JO - Nonlinearity
JF - Nonlinearity
IS - 2
M1 - 005
ER -