Calculus of Variations and Geometric Measure Theory

A. Brancolini - S. Solimini

Fractal regularity results on optimal irrigation patterns

created by brancolin on 26 Sep 2017


Published Paper

Inserted: 26 sep 2017

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


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