Published Paper
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Inserted: 26 mar 2004
Last Updated: 9 nov 2026

Journal: J. Math. Sciences (N.Y.)
Volume: 122
Number: 3
Pages: 105-122
Year: 2004

Abstract:

The paper deals with one-dimensional networks of finite length in $\mathbb R^n$ minimizing average distance and maximum distance functionals subject to constraint on the length. We prove that under natural conditions on problem data such minimizers must use maximum available length, cannot contain closed loops (homeomorphic images of a circumference $\mathbb S^1$) and have some mild regularity properties.

Keywords: average distance functional, maximum distance functional, transportation networks

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