Calculus of Variations and Geometric Measure Theory

M. Goldman

Self-similar minimizers of a branched transport functional

created by goldman on 10 Apr 2017
modified on 20 Jun 2018


Accepted Paper

Inserted: 10 apr 2017
Last Updated: 20 jun 2018

Journal: Indiana
Year: 2018


We solve here completely an irrigation problem from a Dirac mass to the Lebesgue measure. The functional we consider is a two dimensional analog of a functional previously derived in the study of branched patterns in type-I superconductors. The minimizer we obtain is a self-similar tree.