Se-Chan Lee

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math.AP2024

Regularity for solutions of non-uniformly elliptic equations in non-divergence form

Jongmyeong Kim, Se-Chan Lee

We prove the Aleksandrov--Bakelman--Pucci estimate for non-uniformly elliptic equations in non-divergence form. Moreover, we investigate local behaviors of solutions of such equati…

math.AP2023

Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth

Minhyun Kim, Se-Chan Lee

We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal non…

math.AP2023

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

Se-Chan Lee, Hyungsung Yun

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 regu…

math.AP2023

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

Ki-Ahm Lee, Se-Chan Lee, Hyungsung Yun

We establish the interior $C^{1, α}$ -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations $u_{t} = ∣ D u ∣^{γ} F (D^{2} u) + f .$ For this purpose, we pr…

Regularity for solutions of non-uniformly elliptic equations in non-divergence form

Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth

C1,α-regularity for functions in solution classes and its application to parabolic normalized p-Laplace equations

C1,α-regularity for solutions of degenerate/singular fully nonlinear parabolic equations

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

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