Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its s urface energy are studied. After elimination of the displacement, the probl em reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is s hown that this functional may have a stable absolute minimum or only a mini mizing sequence in which the term corresponding to the bulk energy is force d to zero by the production of a crack in the material.