Existence of solutions to boundary value problems for smectic liquidcrystals

We prove lower semicontinuity and lower bounds for aChen-Lubensky energy describing nematic/smectic liquid crystals withphysically realistic boundary conditions. The Chen-Lubensky energycaptures stable phases of the liquid crystal material, ranging frompurely nematic or smectic states to coexisting nematic/smecticstates. By including appropriate additional terms, the modelincludes the effects of applied electric or magnetic fields, and/orelectrical self-interactions in the case of polarized liquidcrystals. As a consequence of our results, we establish existenceof minimizers with weak or strong anchoring of the director field(describing molecular orientation) at the boundary, and Dirichlet orNeumann boundary conditions on the smectic order parameter for theliquid crystal material.