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Publication 09-CNA-11

Nonlocal Character of the Reduced Theory of Thin Films with Higher Order Perturbations

G. Dal Maso
SISSA
Via Beirut 2
34151 Trieste, Italy
dalmaso@sissa.it

Irene Fonseca
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Giovanni Leoni
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213
giovanni@andrew.cmu.edu

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

\begin{displaymath}u \mapsto \int_{\Omega}f(u,Du)\ dx\end{displaymath}

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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