Abstract
In place of flows on a discrete network we study flows described by a vector field σ(x,y) in a plane domain ω. The analogue of the capacity constraint is |σ|≤c(x,y), and the strength of sources and sinks is σ·n=λf on the boundary and—div σ=λF in the interior. We show that the largest λ (the maximal flow) is determined by the minimal cut. As in the discrete case the dual problem has a 0–1 solution, given by the characteristic function of the minimal cut; for the continuous problem the argument depends on the coarea formula for functions of bounded variation.
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Strang, G. Maximal flow through a domain. Mathematical Programming 26, 123–143 (1983). https://doi.org/10.1007/BF02592050
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DOI: https://doi.org/10.1007/BF02592050