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.
Part of this work was carried out while visiting Filippo Cagnetti, whom I thank for the kind hospitality, at the Instituto Superior Técnico in Lisbon. I am also very grateful to Massimiliano Morini for multiple valuable discussions.
© 2015 by De Gruyter