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.

14 pages, we add the discussion on our results for global minimizers, and all comments are welcome!