2.00 pm, Lecture Hall 6
Influence of the geometry on the onset of superconductivity
The onset of superconductivity is governed by the ground state of magnetic Laplacian operators. The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in smooth three-dimensional domains is characterized by model problems inside the domain or on its boundary. In two-dimensional polygonal domains, a new set of model problems on sectors has to be taken into account. In this talk, we consider the class of general corner domains. In dimension 3, they include as particular cases polyhedra and axisymmetric cones. We attach model problems not only to each point of the closure of the domain, but also to a hierarchy of ``tangent substructures'' associated with singular chains.
This is a joint work with M. Dauge and N. Popoff.