Primal Dual model in the continuous domain

The continuous max flow problem is posed as follows :

sup $\int_\Omega p_s(x)dx$

subject to :

$|p(x)| \le C(x); \forall x \in \Omega$

$p_s(x) \le C_s(x); \forall x \in \Omega$

$p_t(x) \le C_t(x); \forall x \in \Omega$

$\nabla \cdot p(x) - p_s(x) + p_t(x) = 0; \forall x \in \Omega$

Here $p(x)$ is a field vector and is analogous to the flow in the discrete domain. $\nabla \cdot p$ is the divergence of the field p.

How do i find out the dual of this maximization problem using the lagrangian dual technique, i.e. the equivalent min cut formulation of the problem in the continuous domain.