Global regularity of parabolic p-Laplace equations on convex domains

We show the global regularity of the nonhomogeneous parabolic p-Laplace equations on convex domains. Starting with the local up-to-boundary Lipschitz regularity for the homogeneous equation, we derive the global a priori estimates via Vitali covering coupling with p-harmonic approximation. Moreover, the exponents in the a priori estimates come from the intrinsic scaling.