Geodesic
Epitaxially strained elastic films: the case of anisotropic surface energies
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 167-189

Voir la notice de l'article provenant de la source Numdam

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. Following the approach of [N. Fusco and M. Morini, Equilibrium configurations of epitaxially strained elastic films: second order minimality conditions and qualitative properties of solutions. Preprint], we obtain these results by means of a minimality criterion based on the positivity of the second variation.

DOI : 10.1051/cocv/2012003
Classification : 74G55, 74K35, 74G65, 49Q20, 49K10
Keywords: epitaxially strained crystalline films, anisotropic surface energy, second order minimality conditions, second variation 
@article{COCV_2013__19_1_167_0,
     author = {Bonacini, Marco},
     title = {Epitaxially strained elastic films: the case of anisotropic surface energies},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {167--189},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     year = {2013},
     doi = {10.1051/cocv/2012003},
     mrnumber = {3023065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012003/}
}
TY  - JOUR
AU  - Bonacini, Marco
TI  - Epitaxially strained elastic films: the case of anisotropic surface energies
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2013
SP  - 167
EP  - 189
VL  - 19
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012003/
DO  - 10.1051/cocv/2012003
LA  - en
ID  - COCV_2013__19_1_167_0
ER  - 
%0 Journal Article
%A Bonacini, Marco
%T Epitaxially strained elastic films: the case of anisotropic surface energies
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 167-189
%V 19
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012003/
%R 10.1051/cocv/2012003
%G en
%F COCV_2013__19_1_167_0
Bonacini, Marco. Epitaxially strained elastic films: the case of anisotropic surface energies. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 167-189. doi: 10.1051/cocv/2012003

Cité par Sources :