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Flows in infinite networks represented by vector lattices

โœ Scribed by B. Fuchssteiner; K. Morisse

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
294 KB
Volume
10
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

We are concerned with minimal cost flows in infinite networks. As an application of a Hahn-Banach type monotone extension theorem for convex cones, an abstract theorem characterizing minimal cost flows by local price systems is obtained for a general vector lattice situation. This result extends the usual finite network result, or rather its extension to some L 1 -L ยฐยฐ situation, which states that the minimal transportation cost is the supremum (taken over all local price systems) of the difference between consumption cost and transportation profit.

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Absolutely Continuous Flows Generated by Sobolev Class Vector Fields in Finite and Infinite Dimensions
โœ Vladimir Bogachev; Eduardo Mayer-Wolf ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 434 KB

We prove the existence of the global flow [U t ] generated by a vector field A from a Sobolev class W 1, 1 (+) on a finite-or infinite-dimensional space X with a measure +, provided + is sufficiently smooth and that a {A and |$ + A| (where $ + A is the divergence with respect to +) are exponentially