  We transfer the celebrating Monge-Kontorovich problem in a bounded domain of
Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear
elliptic equation with $0-$order term missing in its diffusion coefficients:
\begin{eqnarray*} A(x, F'_x)F''_{xx}+B(y, F'_y)F''_{yy}&=&C(x, y, F'_x, F'_y)
\end{eqnarray*} where $A(.,.)>0, B(.,.)>0$ and $C$ are functions based on the
initial distributions, $F$ is an unknown probability distribution function and
therefore closed the former problem.
