Calculus of Variations and Geometric Measure Theory

M. Bonacini

Stability of equilibrium configurations for elastic films in two and three dimensions

created by bonacini on 07 Aug 2013
modified on 12 May 2015


Published Paper

Inserted: 7 aug 2013
Last Updated: 12 may 2015

Journal: Adv. Calc. Var.
Volume: 8
Number: 2
Pages: 117-153
Year: 2015
Doi: 10.1515/acv-2013-0018


We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

Keywords: second variation, Epitaxially strained elastic films, Local minimality