Energetics of fine domain structures

In the last two decades, numerous new mathematical tools have emerged in the literature on Calculus of Variations for the analysis of minimization problems involving non-convex free-energies. These advances have shed some new light on the behavior of a variety of physical systems exhibiting domain structures, and on their response to external actions (forces, electromagnetic fields, etc.). Examples range from ferroelastic solids, and, in particular, shape memory alloys, to ferromagnetic and ferroelectric materials, and, in particular, solids with strong electro- or magneto-elastic coupling. In this paper, some of these mathematical techniques are applied to analyze experimental and theoretical observations of striped domain patterns in liquid crystalline polymers.