Existence of Solutions to Boundary Value Problems for Smectic Liquid Crystals Patricia Bauman * , and Daniel Phillips † Department of Mathematics Purdue University West Lafayette, IN 47906 bauman@math.purdue.edu phillips@math.purdue.edu Jinhae Park ‡ Department of Mathematics Chungnam National University 220 Kung-Dong, Yuseong-Gu Daejeon 305-763, South Korea, jhpark2003@gmail.com May 2, 2013 Abstract We prove lower semicontinuity and lower bounds for a Chen-Lubensky energy describing nematic/smectic liquid crystals with physically re- alistic boundary conditions. The Chen-Lubensky energy captures sta- ble phases of the liquid crystal material, ranging from purely nematic or smectic states to coexisting nematic/smectic states. By including appropriate additional terms, the model includes the effects of ap- plied electric or magnetic fields, and/or electrical self-interactions in the case of polarized liquid crystals. As a consequence of our results, we establish existence of minimizers with weak or strong anchoring of the director field (describing molecular orientation) at the boundary, and Dirichlet or Neumann boundary conditions on the smectic order parameter for the liquid crystal material. * Research supported by NSF grant DMS-1109459 † Research supported by NSF grant DMS-1109459 ‡ Research supported by NRF of Korea with grant number 2011-0014882 1