Variational approximation of functionals defined on 1-dimensional connected sets: the planar case

13 Oct 2018 Bonafini Mauro Orlandi Giandomenico Oudet Edouard

In this paper we consider variational problems involving 1-dimensional connected sets in the Euclidean plane, such as the classical Steiner tree problem and the irrigation (Gilbert-Steiner) problem. We relate them to optimal partition problems and provide a variational approximation through Modica-Mortola type energies proving a $\Gamma$-convergence result... (read more)

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  • OPTIMIZATION AND CONTROL
  • ANALYSIS OF PDES