Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit

Abstract: We investigate the vanishing elasticity limit for minimizers of the Landau-de Gennes model with finite energy. By adopting a refined blow-up and covering analysis, we establish the optimal $ L^p $ ($ 1<p<\infty $) convergence of minimizers and achieve the sharp $ L^1 $ convergence rate of the bulk energy term.