Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s

We prove pointwise gradient bounds for entire solutions of pde’s of the form ℒu(x) = ψ(x, u(x), ∇u(x)) ,where ℒ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J. Serrin are also recovered as particular cases of our approach.