Calculus of Variations and Geometric Measure Theory
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A. Brancolini - S. Solimini

Fractal regularity results on optimal irrigation patterns

created by brancolin on 24 Apr 2013
modified on 23 Sep 2015

[BibTeX]

Published Paper

Inserted: 24 apr 2013
Last Updated: 23 sep 2015

Journal: J. Math. Pures Appl.
Volume: 102
Pages: 854-890
Year: 2014
Doi: 10.1016/j.matpur.2014.02.008

Abstract:

In this paper the problem of the regularity of the minima of the branched transport problem is addressed. We show that, under suitable conditions on the irrigated measure, the minima present a fractal regularity, that is on a given branch of length $l$ the number of branches bifurcating from it whose length is comparable with $\varepsilon$ can be estimated both from above and below by $l/\varepsilon$.

Keywords: optimal transport problem, landscape function, irrigation problem, branched transport problem, fractal regularity

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