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
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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