Abstract
The general Monge-Kantorovich problem consists in the computation of the optimal value where the cost function and the measure on with are assumed to be given, is the cone of finite positive Borel measures on , and and are the projections on the first and second coordinates, which assign to a measure the corresponding marginal measures. An explicit formula is obtained for in the case when is a domain in and is bounded, vanishes on the diagonal, and is continuously differentiable in a neighborhood of the diagonal. Conditions for the set to be nonempty are investigated, and with their help new characterizations of cyclically monotone mappings are obtained.
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