Inserted: 26 mar 2004
Last Updated: 24 mar 2017
Journal: J. Math. Sciences (N.Y.)
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