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We consider two variational models for transport networks, an urban planningand a branched transport model, in both of which there is a preference fornetworks that collect and transport lots of mass together rather thantransporting all mass particles independently. The strength of this preferencedetermines the ramification patterns and the degree of complexity of optimalnetworks. Traditionally, the models are formulated in very different ways, viacost functionals of the network in case of urban planning or via costfunctionals of irrigation patterns or of mass fluxes in case of branchedtransport. We show here that actually both models can be described by all threetypes of formulations; in particular, the urban planning can be cast into aEulerian (flux-based) or a Lagrangian (pattern-based) framework.

Equivalent formulations for the branched transport and urban planning problems