Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
Eric Bonnetier, Richard S. Falk, Michael A. Grinfeld (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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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...