O'Reilly logo

Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Paul Pegon

11 On the Lagrangian branched transport model and the equivalence with its Eulerian formulation

Paul Pegon, Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, 91405 Orsay Cedex, France, paul.pegon@math.u-psud.fr

Abstract: First, we present two classical models of branched transport: the Lagrangian model introduced by Bernot et al. and Maddalena et al. [3, 7], and the Eulerian model introduced by Xia [13]. An emphasis is put on the Lagrangian model, for which we give a complete proof of existence of minimizers in a – hopefully – simplified manner. We also treat in detail some σ-finiteness and rectifiability issues to yield rigorously the energy formula connecting the irrigation cost Iα to the Gilbert energy Eα. Our main purpose ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required