Second order Sobolev regularity results for the generalized p-parabolic equation
arxiv(2024)
摘要
We study a general class of parabolic equations
u_t-|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
L^2-integrable Sobolev time derivative.
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