Inserted: 24 apr 2013
Last Updated: 23 sep 2015
Journal: J. Math. Pures Appl.
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