Second order Sobolev regularity results for the generalized
$p$-parabolic equation
Second order Sobolev regularity results for the generalized
$p$-parabolic equation
We study a general class of parabolic equations $$ u_t-|Du|^\gamma\big(\Delta u+(p-2) \Delta_\infty^N u\big)=0, $$ 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 …