\documentclass[12pt]{article} 
\begin{document} 

\begin{center} 

{\bf \large Nonlocal Character of the Reduced Theory of Thin Films with Higher Order Perturbations} 

\vspace{.10in} 

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

\vspace{.10in}

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

\vspace{.10in} 

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

\end{center} 

\vspace{.15in} 

\noindent {\bf 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 

$$ u \mapsto \int_{\Omega}f(u,Du)\ dx$$

\noindent 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.

\end{document} 