5 papers
Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations
Hyungsung Yun
We study boundary regularity of viscosity solutions to fully nonlinear degenerate or singular parabolic equations. The gradient-dependent degeneracy or singularity, along with the…
Boundary Hölder gradient estimates for parabolic -Laplace type equations
Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun +1
In this paper, we study the boundary regularity for viscosity solutions of parabolic -Laplace type equations. In particular, we obtain the boundary pointwise regulari…
Optimal regularity for degenerate parabolic equations on a flat boundary
Hyungsung Yun
We establish the optimal regularity of viscosity solutions to \begin{equation*} u_t - x_n^γÎu = f, \end{equation*} which arises in the regularity theory for the porous medium equ…
Time derivative estimates for parabolic -Laplace equations and applications to optimal regularity
Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun +1
We establish the boundedness of time derivatives of solutions to parabolic -Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximat…
Regularity theory for fully nonlinear equations of porous medium-type
Hyungsung Yun
In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet…