Abstract for the talk on 15.11.2022 (16:45 h)

Oberseminar ANALYSIS - PROBABILITY

Michael Goldman (Universite de Paris, LJLL)
From local energy bounds to dimensional estimates in a reduced model for type-I superconductors
15.11.2022, 16:45 h, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)

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.

 

29.08.2022, 11:25