Liquid Crystals and Energy Estimates for S2-Valued Maps

This report summarizes results obtained in collaboration with J.M. Coron and E. Lieb (see [3] and [4]); it answers some questions raised by J. Ericksen and D. Kinderlehrer. The original motivation comes from the theory of liquid crystals (see [7], [8], [10]), and is well explained in other contributions to this volume.