Facilities 发表于 2025-3-27 00:40:24
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Interior and Boundary Regularity,point .∈. (Section 8.2). These definitions and the fact that connected components of an optimal traffic plan are themselves optimal traffic plans will permit to perform some surgery leading to the main regularity theorems. The first “interior” regularity theorem (Section 8.3) states that outside theJejune 发表于 2025-3-27 10:55:17
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Irrigability and Dimension,s irrigable with respect to α. In that case, notice that μ is also β-irrigable for β>α. This observation proves the existence of a critical exponent α associated with μ and defined as the smallest exponent such that μ is α-irrigable. The aim of the chapter is to link this exponent to more classicalinterpose 发表于 2025-3-27 18:17:15
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The Gilbert-Steiner Problem, setting by Gilbert in . Following his steps, we first consider the irrigation problem from a source to two Dirac masses. If the optimal structure is made of three edges, the first order condition for a local optimum yields constraints on the angles between the edges at the bifurcation point (se贿赂 发表于 2025-3-28 02:45:04
Dirac to Lebesgue Segment: A Case Study,ase of Monge-Kantorovich transport, as illustrated by Figure 13.1, an optimal traffic plan is totally spread in the sense that fibers connect every point of the segment with the source. If α=0, which corresponds to the problem of Steiner, an optimal traffic plan is such that all the mass is first co妨碍 发表于 2025-3-28 10:16:05
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