Epitaxially strained elastic films: the case of anisotropic surface energies

Marco Bonacini

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 1, page 167-189
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Bonacini, Marco. "Epitaxially strained elastic films: the case of anisotropic surface energies." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 167-189. <http://eudml.org/doc/272806>.

@article{Bonacini2013,
abstract = {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.},
author = {Bonacini, Marco},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {epitaxially strained crystalline films; anisotropic surface energy; second order minimality conditions; second variation},
language = {eng},
number = {1},
pages = {167-189},
publisher = {EDP-Sciences},
title = {Epitaxially strained elastic films: the case of anisotropic surface energies},
url = {http://eudml.org/doc/272806},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 1
SP - 167
EP - 189
AB - 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.
LA - eng
KW - epitaxially strained crystalline films; anisotropic surface energy; second order minimality conditions; second variation
UR - http://eudml.org/doc/272806
ER -

References

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