Maximum estimates for solutions of degenerate parabolic equations in divergence form (Q1336327)

Boundedness (in the maximum norm) of solutions of very general nonuniformly parabolic equations is proved. The general form of the estimates is such that the maximum over some space-time cylinder is bounded in terms of some integral over a large cylinder. Several previous results of this type are generalized and improved here. The equations under consideration include anisotropic and doubly degenerate equations.