2013/07/31 by Dmitry Golovaty, Alberto Montero · 1 citation
Mathematics · #math.AP #msc:49N #msc:49S
paper · pdf · doi:10.1007/s00205-014-0731-3
arxiv created 2014/03/27 · arxiv updated 2015/06/16
We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain Ω with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational distribution of rod-like molecules of a nematic liquid crystal. Under the assumption that the energy depends on a single parameter---a dimensionless elastic constant \eps>0---we establish that, as \eps→0, the minimizers converge to a projection-valued map that minimizes the Dirichlet integral away from a single point in Ω. We also provide a description of the limiting map.