Involving the Plateau's problem, we have a property about the functional area which is:

$$\int_{\Omega}\sqrt{1+\mid Du \mid^{2}}dx=\sup\lbrace \int_{\Omega}(g_{n+1} + u\, \text{div} g)dx; g\in C_{C}^{1}(\Omega;\mathbb R^{n+1}), \mid \mid g \mid \mid \leq 1 \rbrace$$ where $u\in W^{1,1}(\Omega)$, $\Omega$ is a domain in $\mathbb R^{n}$.

Please, could you show me more precisely how to prove the above equation from the fact that:

$$\int_{\Omega^{'}}\mid Dv \mid dx=\sup\lbrace \int_{\Omega^{'}}(v\, \text{div} g)dx; g\in C_{C}^{1}(\Omega^{'};R^{n+1}), \mid \mid g \mid \mid \leq 1 \rbrace$$ where $\Omega^{'}$ is a domain in $\mathbb R^{n+1}$ and $v\in W^{1,1}(\Omega^{'})$.


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