Fractal regularity results on optimal irrigation patterns

Brancolini A., Solimini S.

Abstract

In this paper the problem of the regularity, i.e. fractal behaviour, 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 ε can be estimated both from above and below by l / ε. © 2014 Elsevier Masson SAS. All rights reserved.