OPTIMIZATION PROBLEMS IN MASS TRANSPORTATION THEORY ...

• if q < 1 + 1/N for every µ 0 and µ 1 thereexists a path giving finite and minimalvalue to the cost J ;• if q ≥ 1 + 1/N there exist measures µ 0(actually a Dirac mass) such that J =+∞ on every nonconstant path startingfrom µ 0 .Open Problems• linking two L q measures in the diffusionunboundedcase;• concentration case in unbounded setting;• Ω unbounded but not necessarily thewhole space;• working with the space W ∞ (Ω);• comparing this model to the ones by Xiaand by Morel, Solimini, . . . ;• numerical computations;• evolution models?63