Continuity of the temperature in a multi-phase transition problem. Part II

Local continuity is established for locally bounded, weak solutions to a doubly non-linear
parabolic equation that models the temperature of a material undergoing a multi-phase transition.
The enthalpy, as a maximal monotone graph of the temperature, is allowed to possess several jumps
and/or infinite derivatives at the transition temperatures. The effect of the p-Laplacian-type diffusion
is also considered. As an application, we demonstrate a continuity result for the saturation in the flow
of two immiscible fluids through a porous medium, when irreducible saturation is present.