Geodesic
On duality theory for non-topological variants of the~mass transfer problem
Sbornik. Mathematics, Tome 188 (1997) no. 4, pp. 571-602

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Duality theorems are proved in a mass formulation for non-topological variants of the mass transfer problem and of related extremal marginal problems. The connection between two types of problem is investigated (problems with fixed difference between the marginal measures, and problems with fixed marginal measures), and a criterion for their equivalence is obtained. 
@article{SM_1997_188_4_a2,
     author = {V. L. Levin},
     title = {On duality theory for non-topological variants of the~mass transfer problem},
     journal = {Sbornik. Mathematics},
     pages = {571--602},
     publisher = {mathdoc},
     volume = {188},
     number = {4},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_4_a2/}
}
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V. L. Levin. On duality theory for non-topological variants of the~mass transfer problem. Sbornik. Mathematics, Tome 188 (1997) no. 4, pp. 571-602. http://geodesic.mathdoc.fr/item/SM_1997_188_4_a2/