ABSTRACT
Of course, the system of three PDEs (1.3) is not easy to study in general, but it is a low-dimensional system for three functions defined in IR2, unlike the original PDE (1.1) that is posed in IR3. Moreover, the last equation for u2 is independent of the others and can be studied separately.† Once this has been solved and a suitable function u2(x, y) has been determined, the rest of (1.3) yields a system of linear elliptic PDEs for u0 and u1 that can be studied by standard techniques.
