Orateur
Description
In this talk I will introduce a branched transport problem with weakly imposed boundary conditions. This problem was first derived as a reduced model for pattern formation in type-I superconductors in [1]. For minima of the reduced model with weak boundary conditions, it is conjectured in [2] that the dimension of the boundary measure is non-integer. The conjecture was linked to local scaling laws in [5]. I will present some recent advances in solving this conjecture. This talk is based on some works with Michael Goldman, Melanie Koser and Felix Otto [3, 4].
[1] S. Conti, M. Goldman, F. Otto, and S. Serfaty. “A branched transport limit of the Ginzburg-
Landau functional”. In: J. Éc. polytech. Math. 5 (2018), pp. 317–375.
[2] S. Conti, F. Otto, and S. Serfaty. Personal communication.
[3] A. Cosenza, M. Goldman, and M. Koser. New dimensional bounds for a branched transport
problem. 2024. arXiv: 2411.14547 [math.AP].
[4] A. Cosenza, M. Goldman, and F. Otto. Concentration phenomena in a branched transport
problem in the half space. In preparation.
[5] G. De Philippis, M. Goldman, and B. Ruffini. From energy bounds to dimensional esti-
mates in a branched transport model for type-I superconductors. 2023. arXiv: 2304.12715
