Topological Optimization and Optimal Transport

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, [e-mail]

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 I_α to the Gilbert energy E_α. Our main purpose ...