We consider the minimization problem for an average distance functional in the plane, among all compact connected sets of prescribed length. For a minimizing set, the blow-up sequence in the neighborhood of any point is investigated. We show existence of the blow up limits and we characterize them, using the results to get some partial regularity statements.

Blow-up of optimal sets in the irrigation problem / Santambrogio, F; Tilli, Paolo. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 15:2(2005), pp. 343-362.

### Blow-up of optimal sets in the irrigation problem

#### Abstract

We consider the minimization problem for an average distance functional in the plane, among all compact connected sets of prescribed length. For a minimizing set, the blow-up sequence in the neighborhood of any point is investigated. We show existence of the blow up limits and we characterize them, using the results to get some partial regularity statements.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/1709948`