Partial Geometric Regularity of Some Optimal Connected Transportation Networks |
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Authors: | E O Stepanov |
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Institution: | (1) Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
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Abstract: | We consider a continuous optimization model of a one-dimensional connected transportation network under the assumption that
the cost of transportation with the use of network is negligible in comparison with the cost of transportation without it.
We investigate the connections between this problem and its important special case, the minimization of the average distance
functional. For the average distance minimization problem we formulate a number of conditions for the partial geometric regularity
of a solution in ℝn with an arbitrary dimension n ⩾ 2. The corresponding results are applied to solutions to the general optimization problem.
Bibliography: 26 titles. Illustrations: 1 Figure.
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Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 129–157. |
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Keywords: | |
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