Jongmyeong Kim

collaborators

3 papers

math.AP2025

Quantitative bounds for HÃ¶lder exponents in the Krylov--Safonov and Evans--Krylov theories

Jongmyeong Kim, Se-Chan Lee

We establish quantitative bounds for HÃ¶lder exponents in the Krylov--Safonov and Evans--Krylov theories when the ellipticity ratio is close to one. Our analysis relies on the Ishi…

math.AP2025

Asymptotic large time behavior of singular entire solutions of the fast diffusion equation

Kin Ming Hui, Jongmyeong Kim

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ , $α = \frac{2 β - 1}{1 - m}$ and $\frac{2}{1 - m} < \frac{α}{β} < \frac{n - 2}{m}$ . We give a new direct proof using fixed point method on the existence of singular…

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…