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