Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
École Polytechnique, 91128 Palaiseau, France.
2 Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA. e-mail:
3 Educational Testing Service, Princeton, NJ, USA. e-mail:
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.
Mathematics Subject Classification: 49S / 73V25
Key words: Equilibrium shape / non-convex energy functional / variational problem.
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