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

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.