Calculus of Variations and Geometric Measure Theory

E. Paolini - E. Stepanov

Qualitative properties of maximum distance minimizers and average distance minimizers in $\mathbf R^n$

created on 26 Mar 2004
modified by paolini on 24 Mar 2017


Published Paper

Inserted: 26 mar 2004
Last Updated: 24 mar 2017

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


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