  The purpose of the present paper is to show few examples of nonlinear PDEs
(mostly with strong geometric features) for which there is a hidden convex
structure. This is not only a matter of curiosity. Once the convex structure is
unrevealed, robust existence and uniqueness results can be unexpectedly
obtained for very general data. Of course, as usual, regularity issues are left
over as a hard post-process, but, at least, existence and uniqueness results
are obtained in a large framework. The paper will address: THE MONGE-AMPERE
EQUATION, THE EULER EQUATION, MULTIDIMENSIONAL HYPERBOLIC SCALAR CONSERVATION
LAWS AND THE BORN-INFELD SYSTEM.
