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

TL;DR

This paper studies the behavior of Landau-de Gennes minimizers as elasticity vanishes, proving optimal convergence in various norms and providing sharp energy convergence rates.

Contribution

It introduces a refined analysis technique that establishes optimal $L^p$ convergence and sharp $L^1$ energy convergence rates for Landau-de Gennes minimizers.

Findings

Optimal $L^p$ convergence of minimizers

Sharp $L^1$ convergence rate of bulk energy

Refined blow-up and covering analysis

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.