# Self-similar minimizers of a branched transport functional

## TL;DR

This paper completely solves a two-dimensional branched transport problem, revealing that the optimal solution is a self-similar tree structure, extending previous models from superconductivity to irrigation problems.

## Contribution

It provides a complete solution to a 2D branched transport problem, identifying the self-similar tree as the minimizer, which is a novel result in the field.

## Key findings

- The optimal transport network is a self-similar tree.
- The problem is a 2D analog of a model from superconductivity.
- The solution is explicitly characterized as a minimizer.

## Abstract

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.