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Yawen Feng

Publications and source records attributed to Yawen Feng.

3 recordsLinked to original sources
arXiv2024

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

We study a general class of parabolic equations $$ u_t-|Du|^γ\big(Δu+(p-2) Δ_\infty^N u\big)=0, $$ 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 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.

math.AP↗
arXiv2023

A systematic approach on the second order regularity of solutions to the general parabolic $p$-Laplace equation

We study a general form of a degenerate or singular parabolic equation $$ u_t-|Du|^γ\big(Δu+(p-2)Δ_\infty^Nu\big)=0 $$ that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that arises from stochastic game theory. We develop a systematic approach to study second order Sobolev regularity and show that $D^2u$ exists as a function and belongs to $L^2_{\text loc}$ for a certain range of parameters. In this approach proving the estimate boils down to verifying that a certain coefficient matrix is positive definite. As a corollary we obtain, under suitable assumptions, that a viscosity solution has a Sobolev time derivative belonging to $L^2_{\text loc}$.

math.AP↗