On minimizers of the 2D Ginzburg-Landau energy with tangential anchoring

We analyze Ginzburg--Landau minimization problems in two dimensions with either a strong or weak" tangential boundary condition. These problems are motivated by experiments in liquid crystal with boundary defects. In the singular limit when the correlation length tends to zero, we show that boundary defects will be observed for weak anchoring, while both boundary and interior vortices are possible for strong anchoring in the first order limit.