Hölder continuity for two-phase flows in porous media

This work is to prove the Holder continuity of the solutions of the degenerate differential equations describing two-phase, incompressible, immiscible flows in porous media. The differential equations allow degeneracy at two end points and the assumption on mild degeneracy is not required in this study. The regularity result is proved by an alternative argument. Uniqueness of the weak solutions of the differential equations is a direct consequence from this Holder continuity.