Titlebook: Optimal Transportation Networks; Models and Theory Marc Bernot,Vicent Caselles,Jean-Michel Morel Book 2009 Springer-Verlag Berlin Heidelber

Headstrong

oxidize

obeisance

混杂人

Cryptic

Open Problems,Problem 15.1. Let . be a sequence of optimal traffic plans such that . is uniformly bounded and . converges to χ. Is χ optimal?

lanugo

单纯

The Tree Structure of Optimal Traffic Plans and their Approximation, point. The presentation here is inspired from [13]. Several techniques come from papers by Xia [94] and Maddalena-Solimini [58]. The proof of the bi-Lipschitz regularity of fibers with positive flow follows [95] and the pruning and theorem is borrowed from Devillanova and Solimini [79]. The monoton

invert

Irrigability and Dimension, happens if α is critical? Corollary 10.16 gives the answer: if any probability measure μ with a bounded supports is α-irrigable, then α>1/.. Thus the .-dimensional Lebesgue measure is not 1−1/. irrigable. Here the presentation and results follow closely Devillanova’s PhD [28] and Devillanova-Solimi

Generosity

The Landscape of an Optimal Pattern, be defined as a path integral along the network from the source to .. does not depend on the path but only on .. Section 11.4 is devoted to a general semicontinuity property of . and Section 11.5 to its Hölder continuity when the irrigated measure dominates Lebesgue on .. The whole chapter follows

pineal-gland

The Gilbert-Steiner Problem,n Gilbert’s article, yet without proof. In the second section, we generalize the construction already made for two masses to any number of masses. More precisely, if we prescribe a particular topology of a tree irrigating . masses from a Dirac mass, we describe a recursive procedure that permits to