New dimensional bounds for a branched transport problem
Analysis of PDEs
2025-11-20 v2
Abstract
We consider a branched transport problem with weakly imposed boundary conditions. This problem arises as a reduced model for pattern formation in type-I superconductors. For this model, it is conjectured that the dimension of the boundary measure is non-integer. We prove this conjecture in a simplified 2D setting, under the (strong) assumption of Ahlfors regularity of the irrigated measure. This work is the first rigorous proof of a singular behaviour for irrigated measures resulting from minimality.
Cite
@article{arxiv.2411.14547,
title = {New dimensional bounds for a branched transport problem},
author = {Alessandro Cosenza and Michael Goldman and Melanie Koser},
journal= {arXiv preprint arXiv:2411.14547},
year = {2025}
}