1. Blow-up of optimal sets in the irrigation problem
- Author
-
Filippo Santambrogio and Paolo Tilli
- Subjects
Discrete mathematics ,Average distance functional ,blow-up limit ,regularity of minimizers ,length constraint ,Sequence ,Plane (geometry) ,Minimization problem ,Set (abstract data type) ,symbols.namesake ,Differential geometry ,Fourier analysis ,symbols ,Point (geometry) ,Geometry and Topology ,Mathematics - 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.
- Published
- 2005
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