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In this short note we announce the main results of  about variational problems involving 1-dimensional connected sets in the Euclidean plane, such as for example the Steiner tree problem and the irrigation (Gilbert–Steiner) problem.
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Mauro Bonafini, Giandomenico Orlandi, Édouard Oudet, Convex relaxation and variational approximation of functionals defined on 1-dimensional connected sets. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 4, pp. 597–606DOI 10.4171/RLM/823