2005/07/12 by G. Wolansky, Wolansky, G.
Mathematics · #70H20 #90c05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:70H20 #msc:90c05
paper · pdf · doi:10.48550/arxiv.math/0507241
18 pages
arxiv created 2005/07/12 · arxiv updated 2009/12/01
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.