| Issue |
ESAIM: M2AN
Volume 33, Number 3, May June 1999
|
|
|---|---|---|
| Page(s) | 573 - 591 | |
| DOI | https://doi.org/10.1051/m2an:1999153 | |
| Published online | 15 August 2002 | |
Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
1
CNRS-CMAP,
École Polytechnique, 91128 Palaiseau, France.
e-mail:
2
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA.
e-mail:
3
Educational Testing Service, Princeton, NJ, USA.
e-mail:
Received:
10
August
1998
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.
© EDP Sciences, SMAI, 1999
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