Remark 2.8. More generally, the main theorem in [30] shows that the Kantorovich duality holds, for instance, for costs of form
Our goal in this section is to present the relation between the support of a coupling γ and optimality in the Monge–Kantorovich problem (2.1). In the following, we will just summarize key results necessary to present recent developments of optimal transportation with Coulomb and repulsive harmonic-type costs.
Roughly speaking, it is well known in optimal transport theory with 2-marginals that for a wide class of costs c, a coupling γ is optimal if, and only if, the support ...
No credit card required