Existence of infinitely many equilibrium configurations of a liquid crystal system prescribing the same nonconstant boundary value

Min-Chun Hong

Vol. 232 (2007), No. 1, 177–206

DOI: 10.2140/pjm.2007.232.177

Abstract

In 1986, Hardt, Kinderlehrer and Lin established the existence and partial regularity of minimizers of the liquid crystal energy with the Oseen–Frank density. Motivated by the earlier results of Bethuel–Brezis–Coron and Riviere on harmonic maps, we prove the existence of infinitely many equilibrium configurations of the liquid crystal energy prescribing the same nonconstant boundary data.

Keywords

liquid crystal, equilibrium configurations, harmonic maps

Mathematical Subject Classification 2000

Primary: 35J50

Secondary: 35Q99

Milestones

Received: 8 June 2006

Revised: 18 February 2007

Accepted: 20 February 2007

Published: 1 September 2007