In this note, we study the boundary regularity of the minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularity in all dimensions n >= 3. In dimension n = 3, this yields full regularity at the boundary, which stands in sharp contrast with the observation of boundary defects in physics works. We also show that, in the cases of weak and strong anchoring, the regularity of the minimizers is inherited from that of their corresponding limit problems. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
展开▼
