REGULARITY OF SOLUTIONS OF A DEGENERATE ELLIPTIC VARIATIONAL PROBLEM

We prove regularity of minimizers of the functional {Mathematical expression} recently suggested by Ericksen [10] for the statics of nematic liquid crystals. We show that, given locally minimizing pairs (s, u), s has a continuous representative, and s, u are smooth outside the set {s=0}. The proof relies upon higher integrability estimates, monotonicity, and decay lemmas. © 1990 Springer-Verlag.