Discontinuous order parameters in liquid crystal theories
  The paper is concerned with various issues surrounding the mathematical description of defects in models of liquid crystals, drawing on experience from solid mechanics. The roles played by a suitable choice of function space and by the growth properties of the free-energy density are highlighted. Models in which the director can jump across surfaces are formulated, and their relevance for nematic elastomers, order reconstruction and smectic A thin films discussed. 
J. M. Ball and S. J. Bedford
math.AP cond-mat.soft