Published Paper

Inserted: 22 jun 2005
Last Updated: 3 may 2011

Journal: Math. Ann.
Volume: 338
Number: 1
Pages: 119-146
Year: 2007

Abstract:

Let $\Omega$ be a $C^2$ bounded open set of $*R*^2$ and consider the functionals $$ F_\varepsilon (u)\;:=\; \int_\Omega \left\{\frac{(1-
\nabla u (x)
^{2)2}{\varepsilon}} + \varepsilon
D² u (x)
^2\right\}\, dx\, . $$ We prove that if $u\in W^{1, \infty} (\Omega)$, $
\nabla u
=1$ a.e., and $\nabla u\in BV$, then $$ \Gamma-\lim_{{\varpesilon\downarrow0}} F_\varepsilon (u)=\frac13 \int_{J{\nabla u}}
\nabla u
³ d\mathcal{H}¹ \, . $$ The new result is the $\Gamma-\limsup$ inequality.

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