Fractal regularity results on optimal irrigation patterns
نویسندگان
چکیده
منابع مشابه
The regularity of optimal irrigation patterns
A branched structure is observable in draining and irrigation systems, in electric power supply systems and in natural objects like the blood vessels, the river basins or the trees. Recent approaches of these networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow s in a river, a road, a tube or a wire, the transportation ...
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This note describes some recent results on the regularity of optimal transport maps. As we shall see, in general optimal maps are not globally smooth, but they are so outside a “singular set” of measure zero. 1. The optimal transportation problem The optimal transportation problem, whose origin dates back to Monge [19], aims to find a way to transport a distribution of mass from one place to an...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2014
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2014.02.008