I want to find $p$ which maximizes the given functional. $p$ is a function of the form $\mathbb{R}^2 \to \mathbb{R}$. $\Omega$ is a region in the 2-d plane.
$\underset{p}{\sup} \int_\Omega \{ \lambda(\vec{\nabla}\cdot \vec{p}) - \alpha(|p| - C)\}\, dx$
Authors of the paper A Study on Continuous Max-Flow and Min-Cut Approaches has said the following to be an equivalent formulation:
$\underset{|p| \le C}{\sup} \int_\Omega \lambda \vec{\nabla}\cdot \vec{p}\, dx$
The authors further claim that it is a well known result that the above is equal to
$\int_\Omega C|\nabla\lambda|\, dx$
And hence it is the desired answer.
I was wondering if I can get the above answer by some more intuitive approach, or if someone could please explain to me what the authors are trying to say.