Existence and regularity results for the Steiner problem

  title={Existence and regularity results for the Steiner problem},
  author={E. Paolini and Eugene O. Stepanov},
  journal={Calculus of Variations and Partial Differential Equations},
  • E. PaoliniE. Stepanov
  • Published 1 March 2013
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
AbstractGiven a complete metric space X and a compact set $${C\subset X}$$ , the famous Steiner (or minimal connection) problem is that of finding a set S of minimum length (one-dimensional Hausdorff measure $${\mathcal H^1)}$$) among the class of sets $$\mathcal{S}t(C) \,:=\{S\subset X\colon S \cup C \,{\rm is connected}\}.$$In this paper we provide conditions on existence of minimizers and study topological regularity results for solutions of this problem. We also study the relationships… 

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Topologie, volume 2. Państwowe

  • Wydawnictwo Naukowe, Warszawa,
  • 1958

Russia E-mail address: stepanov.eugene@gmail