Nonlocal character of the reduced theory of thin films with higher order perturbations
Gianni Dal Maso, Irene Fonseca, Giovanni Leoni · Advances in Calculus of Variations · 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 ↦ ∫ Ω ƒ( u, Du ) 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.