Mathematics – Analysis of PDEs
Scientific paper
2005-07-12
Mathematics
Analysis of PDEs
18 pages
Scientific paper
The extended principle of minimal action is described in the presence of prescribed source and sink points. Under the assumption of zero net flux, it leads to an optimal Monge-Kantorovich transport problem of metric type. We concentrate on action corresponding to a mecahnical Lagrangian. The optimal solution turns out to be a measure supprted on a graph composed of geodesic arcs connecting pairs of sources and sinks.
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