# Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

Eric Bonnetier; Richard S. Falk; Michael A. Grinfeld

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 3, page 573-591
- ISSN: 0764-583X

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topBonnetier, Eric, Falk, Richard S., and Grinfeld, Michael A.. "Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal." ESAIM: Mathematical Modelling and Numerical Analysis 33.3 (2010): 573-591. <http://eudml.org/doc/197404>.

@article{Bonnetier2010,

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.
},

author = {Bonnetier, Eric, Falk, Richard S., Grinfeld, Michael A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Equilibrium shape; non-convex energy functional; variational problem.; minimization of nonconvex nonlocal functional; equilibrium configurations; one-dimensinal variational model; bulk energy; deformable crystal; surface energy; stable absolute minimum; minimizing sequence},

language = {eng},

month = {3},

number = {3},

pages = {573-591},

publisher = {EDP Sciences},

title = {Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal},

url = {http://eudml.org/doc/197404},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Bonnetier, Eric

AU - Falk, Richard S.

AU - Grinfeld, Michael A.

TI - Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 3

SP - 573

EP - 591

AB -
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.

LA - eng

KW - Equilibrium shape; non-convex energy functional; variational problem.; minimization of nonconvex nonlocal functional; equilibrium configurations; one-dimensinal variational model; bulk energy; deformable crystal; surface energy; stable absolute minimum; minimizing sequence

UR - http://eudml.org/doc/197404

ER -

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