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arXiv · 2411.14547

New dimensional bounds for a branched transport problem

Alessandro Cosenza·Michael Goldman·Melanie Koser
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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 behaviour for irrigated measures resulting from minimality.

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Alessandro Cosenza, Michael Goldman, Melanie Koser. 2024-11-21. New dimensional bounds for a branched transport problem. https://arxiv.org/abs/2411.14547

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