Author

Se-Chan Lee

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Open access 2023

$C^{1, α}$-regularity for functions in solution classes and its application to parabolic normalized $p$-Laplace equations

We establish the global $C^{1, α}$-regularity for functions in solution classes, whenever ellipticity constants are sufficiently close. As an application, we derive the global regularity result concerning the parabolic normalized $p$-Laplace equations, provided that $p$ is close to 2. Our analysis relies on the compact...

Se-Chan Lee, Hyung-Gu Yun · arXiv.org · 1 citation

Preprint Sep 2026

Time derivative estimates for normalized parabolic $p$-Laplace equations

We establish the local boundedness of time derivatives of bounded viscosity solutions to the normalized parabolic $p$-Laplace equation for every $p\in(1,\infty)$. The proof combines a logarithmic Bernstein argument with quantitative stability to derive a recursive estimate between different regularizations. For $p=1$ a...

Se-Chan Lee, Hyung-Gu Yun · 0 citations

Open access 2023

$C^{1, α}$-regularity for solutions of degenerate/singular fully nonlinear parabolic equations

We establish the interior $C^{1,α}$-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations $$u_t = |Du|^γF(D^2u) + f.$$ For this purpose, we prove the well-posedness of the regularized Dirichlet problem \begin{equation*} \left\{ \begin{aligned} u_t&=(1+|Du|^2)^{γ/2}F(D^2u) &&\text{i...

Ki-ahm Lee, Se-Chan Lee, Hyung-Gu Yun · arXiv.org · 2 citations