1 citations · 1 across the 4 of their papers we have counts for
7 papers
Lipschitz Regularity in Vectorial Linear Transmission Problems
Alessio Figalli, Sunghan Kim, Henrik Shahgholian
We consider vector-valued solutions to a linear transmission problem, and we prove that Lipschitz-regularity on one phase is transmitted to the next phase. More exactly, given a so…
Nodal Sets for Broken Quasilinear Partial Differential Equations with Dini Coefficients
Sunghan Kim
This paper is concerned with the nodal set of weak solutions to a broken quasilinear partial differential equation, \begin{equation*} \mbox{div} (a_+ \nabla u^+ - a_- \nabla u^-) =…
Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
Marius Ghergu, Sunghan Kim, Henrik Shahgholian
We study the semilinear elliptic equation \begin{equation*} -Δu=u^α|\log u|^β\quad\text{in }B_1\setminus\{0\}, \end{equation*} where with , $\frac…
Isolated Singularities for Semilinear Elliptic Systems with Power-Law Nonlinearity
Marius Ghergu, Sunghan Kim, Henrik Shahgholian
We study the system with , where , , is a nonnegative function tha…
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…