Optimal mass transportation and Mather theory | Zendy

Patrick Bernard | Zendy; Boris Buffoni | Zendy

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Optimal mass transportation and Mather theory

Author(s) -

Patrick Bernard,

Boris Buffoni

Publication year - 2007

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/74

Subject(s) - mathematics , lipschitz continuity , lamination , mass transportation , transportation theory , mass transport , action (physics) , manifold (fluid mechanics) , measure (data warehouse) , function (biology) , lagrangian , absolute continuity , mathematical analysis , computer science , public transport , mechanical engineering , chemistry , physics , organic chemistry , engineering physics , layer (electronics) , biology , engineering , political science , law , quantum mechanics , database , evolutionary biology

We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are inspired from Mather theory on Lagrangian systems. We make use of viscosity solutions of the associated Hamilton-Jacobi equation in the spirit of Fathi's approach to Mather theory

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