Second order Sobolev regularity results for the generalized p-parabolic equation

We study a general class of parabolic equations uₜ-|Du|^γ(Δ u+(p-2) Δ_∞N u)=0, which can be highly degenerate or singular. This class contains as special cases the standard parabolic p-Laplace equation and the normalized version that arises from stochastic game theory. Utilizing the systematic approach developed in our previous work we establish second order Sobolev regularity together with a priori estimates and improved range of parameters. In addition we derive second order Sobolev estimate for a nonlinear quantity. This quantity contains many useful special cases. As a corollary we also obtain that a viscosity solution has locally L²-integrable Sobolev time derivative.