Abstract for the talk on 15.11.2022 (15:15 h)
Oberseminar ANALYSIS - PROBABILITYMichael Goldman (Universite de Paris, LJLL)
From local energy bounds to dimensional estimates in a reduced model for type-I superconductors
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 from 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.