Global gradient estimates for nonlinear parabolic operators

We consider a parabolic equation driven by nonlinear diffusive operator and we obtain gradient estimate in the domain where takes place. This depends on structural constants of equation, geometry ambient space initial boundary data. As byproduct, one easily obtains universal interior estimate, not depending The setting taken into account includes sourcing terms general diffusion coefficients. results are new, to best our knowledge, even Euclidean setting, though treat here also case complete Riemannian manifold.