Abstract. In this talk we focus our attention on problems involving one dimensional sets, using as guiding example the Euclidean Steiner tree problem. We first reformulate the problem over a suitable family of rank one tensor valued measures and then we take two different perspectives. In the first case we focus on the planar setting and provide a variational approximation via Gamma convergence by means of functionals of phase transition type. In the second case we describe a convex framework associated to the problem which provides relevant tools extensively used from a numerical point of view to identify optimal 1d structures.
This is joint work with Giandomenico Orlandi (Verona) and Edouard Oudet (Grenoble).