23 citations · 31 across the 16 of their papers we have counts for
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Higher Order Convergence Rates in Theory of Homogenization III: viscous Hamilton-Jacobi Equations
Sunghan Kim, Ki-Ahm Lee
In this paper, we establish the higher order convergence rates in periodic homogenization of viscous Hamilton-Jacobi equations, which is convex and grows quadratically in the gradi…
Nodal Sets for "Broken" Quasilinear PDEs
Sunghan Kim, Ki-Ahm Lee, Henrik Shahgholian
We study the local behavior of the nodal sets of the solutions to elliptic quasilinear equations with nonlinear conductivity part, \begin{equation*} \operatorname{div}(A_s(x,u)\nab…
Nondivergence elliptic and parabolic problems with irregular obstacles
Sun-Sig Byun, Ki-Ahm Lee, Jehan Oh +1
We prove the natural weighted Calderón and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irr…
The Regularity Theory for the Double Obstacle Problem
Ki-ahm Lee, Jinwan Park, Henrik Shahgholian
In this paper, we prove local regularity of free boundaries for the double obstacle problem with an upper obstacle , \begin{align*} Δu &=fχ_{Ω(u) \cap\{ u< ψ\} }+ Δψχ_{Ω…
Higher Order Convergence Rates in Theory of Homogenization II: Oscillatory Initial Data
Sunghan Kim, Ki-Ahm Lee
We establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems accompanied with rapidly oscillating initial data. Suc…