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 crystals with boundary defects. The imposition of classical boundary conditions on a liquid crystal surface is referred to as “strong anchoring”, while “weak anchoring” refers to the inclusion of boundary energy terms. In the singular limit when the correlation …