Calculus of Variations and Geometric Measure Theory
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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

[BibTeX]

Published Paper

Inserted: 9 sep 2009
Last Updated: 27 jul 2011

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

Abstract:

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.


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