Title:         Analysis of a One-dimensional Variational Model of
               the Equilibrium Shape of a Deformable Crystal

Authors:       Eric Bonnetier, Richard S. Falk, and Michael A. Grinfeld

Source:        M2AN Math. Model. Anal. Numer. 33 (1999), pp. 573-591

Status:        Published

Abstract:      The equilibrium configurations of a one-dimensional variational
               model that combines terms expressing the bulk energy of a
               deformable crystal and its surface energy are studied.  After
               elimination of the displacement, the problem 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 shown that this functional may have
               a stable absolute minimum or only a minimizing sequence in
               which the term corresponding to the bulk energy is forced to
               zero by the production of a crack in the material.

Keywords:      Equilibrium shape, non-convex energy functional, variational
               problem


URL:           http://www.math.rutgers.edu/~falk/papers/vmesdc.pdf