In the limit of vanishing but moderate external magnetic field, we derived a few years ago together with S. Conti, F. Otto and S. Serfaty a branched transport problem f rom the full Ginzburg-Landau model. In this regime, the irrigated measure is the Lebesgue measure and, at least in a simplified 2d setting, it is possible to prove that the minimizer is a self-similar branching tree. In the regime of even smaller magnetic fields, a similar limit problem is expected but this time the irrigation of the Lebesgue measure is not imposed as a hard constraint but rather as a penalization. While an explicit computation of the minimizers seems here out of reach, I will present some ongoing project with G. De Philippis and B. Ruffini relating local energy bounds to dimensional estimates for the irrigated measure.
From local energy bounds to dimensional estimates in a reduced model for type-I superconductors
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Nom de l'orateur
Michael Goldman
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Laboratoire Jacques-Louis Lions (LJLL)
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