Thin film liquid crystals with oblique anchoring and boojums

We study a two-dimensional variational problem which arises as a thin-film limit of the Landau–de Gennes energy of nematic liquid crystals. We impose an oblique angle condition for the nematic director on the boundary, via boundary penalization (weak anchoring.) We show that for strong anchoring strength (relative to the usual Ginzburg–Landau length scale parameter), defects will occur in the interior, as in the case of strong (Dirichlet) …