Calculus of Variations and Geometric Measure Theory

F. Santambrogio - P. Tilli

Blow-up of Optimal Sets in the Irrigation Problem

created on 26 Aug 2004
modified by santambro on 10 Sep 2005


Published Paper

Inserted: 26 aug 2004
Last Updated: 10 sep 2005

Journal: J. Geom. Anal.
Volume: 15
Number: 2
Pages: 343-362
Year: 2005


We consider the minimization problem for an average distance functional in the plane, among all compact connected sets of prescribed length, as proposed by Buttazzo, Oudet and Stepanov. For a minimizing set, the blow-up sequence in the neighbourhood 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. In particular we get $C^{1,1}$ regularity near triple junctions.

Keywords: regularity, average distance functional