A nonlinear version of the Kantorovich–Rubinstein maximum principle Original Research Article

The classical Kantorovich–Rubinstein theory gives necessary conditions for maxima of linear functionals acting on the space of Lipschitzian functions. We show analogous results for some nonlinear functionals of Hammerstein type. Our proofs are based on theorems concerning local changes of Lipschitzian functions similar to the McShane extension theorem.