OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS

By Qinglan Xia. 2003

166 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/32c4c163c77f51a15bdb3d3a58561c03ac315954

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A Modica-Mortola Approximation for Branched Transport and Applications (2011, methodology): “Xia on (see [27]) that the energy M is obtained as a relaxation of the same energy defined on finite graphs.”
The structure of branched transportation networks (2008, methodology): “The following lemma and proposition were proved in [ 21 ] and their proofs adapt immediately to traffic plans.”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “Maddalena, Solimini [221, 222] for the Lagrangian model, and by Xia [297], who gave an Eulerian continuous extension of the Gilbert Energy.”
A variational model of irrigation patterns (2003, background): “This paper is not, however, the first mathematical attempt and we know of two other works addressing the existence problem, namely [5] and [29].”
A User’s Guide to Optimal Transport (2013, background): “In [81], [60] and [15] the existence of an optimal branched transport (Theorem 5.”
The Geodesic Problem in Quasimetric Spaces (2008, background): “21 In [10], we defined dα(a,b) := min{Mα(G) : G ∈ Path(a,b)} for 0 ≤ α < 1 and showed that dα defines a metric on the space of (atomic) probability measures.”
Interior regularity of optimal transport paths (2004, methodology): “In [12], we showed that for any polyhedral 1-chain P , there exists a polyhedral 1-chain P̃ with ∂P̃ = ∂P such that P̃ contains no 1-cycles in its support and M ( P̃ ) ≤ M (P ).”