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We study a general class of parabolic equations uₜ-|Du|^ (u+ (p-2) _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.
Feng et al. (Tue,) studied this question.
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