# On the well-posedness of branched transportation

## TL;DR

This paper proves the stability of optimal traffic paths in branched transport, demonstrating that limits of optimal paths remain optimal, thus resolving a previously open problem in the field.

## Contribution

It establishes the full generality of stability results for optimal traffic paths in branched transport, removing previous restrictive assumptions.

## Key findings

- Limit of optimal traffic paths is optimal
- Addresses an open problem in branched transport stability
- Provides a general proof applicable to broad cases

## Abstract

We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book Optimal transportation networks, by Bernot, Caselles and Morel), which has been addressed up to now only under restrictive assumptions.