9 citations · 16 across the 13 of their papers we have counts for
13 papers
Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems
Sunghan Kim, Kaj Nyström
We prove new optimal regularity results for obstacle problems involving evolutionary -Laplace type operators in the degenerate regime . Our main results include…
Constraint maps with free boundaries: the obstacle case
Alessio Figalli, Sunghan Kim, Henrik Shahgholian
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part…
Uniform Integrability in Periodic Homogenization of Fully Nonlinear Equations
Sunghan Kim
This paper is devoted to the study of uniform - and -estimates for viscosity solutions to fully nonlinear, uniformly elliptic, periodic homogenizatio…
A transmission problem for -Laplacian
Maria Colombo, Sunghan Kim, Henrik Shahgholian
In this paper, we consider a double-phase problem characterised by a transmission that takes place across the zero level "surface" of the minimiser of the functional $$ J(v,Ω) = \i…
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…
Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations
Sunghan Kim, Ki-Ahm Lee
This article is concerned with uniform and estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness…
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…
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…
An Elliptic Free Boundary Arising From the Jump of Conductivity
Sunghan Kim, Ki-ahm Lee, Henrik Shahgholian
In this paper we consider a quasilinear elliptic PDE, , where the underlying physical problem gives rise to a jump for the conductivity , a…