Calculus of Variations and Geometric Measure Theory

G. Dal Maso - I. Fonseca - G. Leoni

Nonlocal character of the reduced theory of thin films with higher order perturbations

created by dalmaso on 09 Sep 2009
modified by leoni on 27 Jul 2011


Published Paper

Inserted: 9 sep 2009
Last Updated: 27 jul 2011

Journal: Adv. Cal. Var.
Volume: 3
Number: 3
Pages: 287-319
Year: 2010


In this paper it is shown that, when there is lack of coercivity with respect to some partial derivatives on the underlying field $u$, then the relaxation of the functional% \[ u\mapsto\int_{\Omega}f\left( u,Du\right) \,dx \] may fail to be local. This result is applied to a singular perturbation model for a membrane energy depending on deformations and out-of-plane bending.