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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Communicated by Steven Bell
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Santambrogio, F., Tilli, P. Blow-up of optimal sets in the irrigation problem. J Geom Anal 15, 343–362 (2005). https://doi.org/10.1007/BF02922199
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DOI: https://doi.org/10.1007/BF02922199