Max-flow min-cut theorem in an anisotropic network
The author gives rigorous formulations of max-flow problems and min-cut problems on a bounded domain in the n-dimensional Euclidean space with Lipschitz boundary. The max-flow problems have anisotropic capacity constraints and contain continuous versions of max-flow problems of \textit{M. Iri} [in: Survey of mathematical programming, Proc. int. Symp., Vol. 2, Budapest 1976, 263-278 (1980; Zbl 0429.90029)] and \textit{G. Strang} [Math. Program. 26, 123-143 (1983; Zbl 0513.90026)]. According to Strang's idea the author takes an essentially bounded vector field as any flow and a subset of the domain such that the characteristic function is a function of bounded variation as any cut and proves that max-flow min- cut theorems for them hold if the capacity constraints satisfy some boundedness condition and continuity condition.
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