Within the framework of inverse Lie problems we give some non–trivial examples of Lie–remarkable equations, i.e., classes of partial differential equations that are in one–to–one correspondence with their Lie point symmetries. In particular, we prove that the second order Monge-Ampere equation in two independent variables is Lie–remarkable. The same property is shared by some classes of second order Monge-Ampere equations involving more than two independent variables, as well as by some classes of higher order Monge-Ampere equations in two independent variables. In closing, also the minimal surface equation in IR is considered.