Sunghan Kim

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20212024

most citedUniform Integrability in Periodic Homogenization of Fully Nonlinear Equations

1 citations · 1 across the 4 of their papers we have counts for

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math.AP2024

Constraint maps and free boundaries

Alessio Figalli, André Guerra, Sunghan Kim +1

In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps.…

math.AP2024

Constraint maps: singularities vs free boundaries

Alessio Figalli, André Guerra, Sunghan Kim +1

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diver…

math.AP2024

Regularity near the fixed boundary for transmission systems

Alessio Figalli, Somayeh Khademloo, Sunghan Kim +1

Given $Ω \subset R^{n}$ with $n \geq 2$ , $D \subset Ω$ open, and $u : Ω \to R^{m}$ , we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)χ_D)\nabla u\big) =…

math.AP2023

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…

math.AP2021★ 1 cited

Uniform Integrability in Periodic Homogenization of Fully Nonlinear Equations

Sunghan Kim

This paper is devoted to the study of uniform $W^{1, \frac{n p}{n - p}}$ - and $W^{2, p}$ -estimates for viscosity solutions to fully nonlinear, uniformly elliptic, periodic homogenizatio…