# Surface Superconductivity in Presence of Corners

Emanuela Giacomelli
(Tübingen)
Math/Phys Seminar
Tuesday, 10 April, 2018, at 15:00-16:00, in Aud. D4 (1531-219)
Abstract:
We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg-Landau minimizer is approximately constant along the transversal direction. To isolate the contributions to the energy density due to the presence of corners we then introduce a new effective problem. The explicit expression of the effective energy is yet to be found, but we formulate a conjecture on it based on the behavior for almost flat angles. Indeed in this case we are able to explicitly compute the leading order of the corners effective problem and show that it sums up to the smooth boundary contribution to reconstruct the same asymptotics as in smooth domains. Joint work with Michele Correggi.
Contact person: Søren Fournais