  We succeed in writing 2-dimensional conformally invariant non-linear elliptic
PDE (harmonic map equation, prescribed mean curvature equations...etc) in
divergence form. This divergence free quantities generalize to target manifolds
without symmetries the well known conservation laws for harmonic maps into
homogeneous spaces. From this form we can recover, without the use of moving
frame, all the classical regularity results known for 2-dimensional conformally
invariant non-linear elliptic PDE . It enable us also to establish new results.
In particular we solve a conjecture by E.Heinz asserting that the solutions to
the precribed bounded mean curvature equation in arbitrary manifolds are
continuous.
