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

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 $L^p$ ($1<p<+\mathrm{\infty }$) convergence of minimizers and achieve the sharp $L^1$ convergence rate of the bulk energy term.