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math.AP2017
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…
math.AP2017★ 1 cited
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…
math.AP2017
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…