Dirichlet problem with prescribed vortices for multiply connected domains (Q2825863)

The paper deals with the reduction of the Dirichlet problem with prescribed vortices for multiply connected domains to the general Riemann-Hilbert boundary problem. The author starts with a short introduction of the problem and gives an overview of the needed mathematical framework as the functional analytic setting. After that, the examination of the solution of the Riemann-Hilbert boundary problem is presented. The focus lies on the minimization of the Ginzburg-Landau functional and the application of the method of successive approximations, which leads to the Poincaré series.NEWLINENEWLINEFor the entire collection see [Zbl 1327.30002].