NEW DIMENSIONAL BOUNDS FOR A BRANCHED TRANSPORT PROBLEM

Alessandro Cosenza; Michael Goldman; Melanie Koser

doi:10.1137/24M1713077

NEW DIMENSIONAL BOUNDS FOR A BRANCHED TRANSPORT PROBLEM

Alessandro Cosenza
, Michael Goldman
, Melanie Koser

UPMC Université de Paris VI
Humboldt-Universität zu Berlin

Research output: Contribution to journal › Article › peer-review

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 behavior for irrigated measures resulting from minimality.

Original language	English
Pages (from-to)	926-959
Number of pages	34
Journal	SIAM Journal on Mathematical Analysis
Volume	58
Issue number	2
DOIs	https://doi.org/10.1137/24M1713077
Publication status	Published - 1 Jan 2026

Keywords

branched transport
fractal dimension
scaling laws

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10.1137/24M1713077

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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 behavior for irrigated measures resulting from minimality.",

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author = "Alessandro Cosenza and Michael Goldman and Melanie Koser",

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N2 - 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 behavior for irrigated measures resulting from minimality.

AB - 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 behavior for irrigated measures resulting from minimality.

KW - branched transport

KW - fractal dimension

KW - scaling laws

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ER -

NEW DIMENSIONAL BOUNDS FOR A BRANCHED TRANSPORT PROBLEM

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