Sunghan Kim
Postdoktor vid Matematiska institutionen; Akademisk personal
- Telefon:
- 018-471 31 86
- E-post:
- sunghan.kim@math.uu.se
- Besöksadress:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postadress:
- Box 480
751 06 UPPSALA
Ladda ned kontaktuppgifter för Sunghan Kim vid Matematiska institutionen; Akademisk personal
Postdoktor vid Matematiska institutionen; Analys och partiella differentialekvationer
- Telefon:
- 018-471 31 86
- E-post:
- sunghan.kim@math.uu.se
- Besöksadress:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postadress:
- Box 480
751 06 UPPSALA
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Kort presentation
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Overall, my research interests lie in analysis of PDEs and related problems in geometry. More specifically:
- Free boundary problems
- Homogenization problems
- Regularity theory
- Degenerate/singular PDEs
- Semilinear problems
Nyckelord
- analysis
- free boundary problems
- homogenization problems
- parabolic pdes
- partial differential equations
- regularity
- semilinear problems
Biografi
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Link to my personal webpage: here
Forskning
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Over the past few years, I have developed great interests in constraint maps, which are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, they manifest a diverse structure that includes singularities similar to harmonic maps, branch points reminiscent of minimal surfaces, and intricate free-boundary behavior of the obstacle problem. The complexity of these maps poses significant challenges to their analysis. This has led me to a series of recent collaborations, which address the following fundamental issue: does the free boundary meet the mapping singularities?
- Constraint maps and free boundaries (with A. Figalli, A. Guerra and H. Shahgholian), an expository article, preprint available at arxiv:2411.04110, 2024
- Constraint maps: singularities vs free boundaries (with A. Figalli, A. Guerra and H. Shahgholian),
preprint available at arXiv:2407.21128, 2024 - Constraint maps with free boundaries: the Bernoulli case (with A. Figalli, A. Guerra and H. Shahgholian),
to appear in J. Eur. Math. Soc., preprint available at arXiv:2311.03006, 2023 - Constraint maps with free boundaries: the obstacle case (with A. Figalli and H. Shahgholian),
Arch. Ration. Mech. Anal., 248 (2024) no. 79.
Publikationer
Senaste publikationer
- Constraint Maps with Free Boundaries (2024)
- Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems (2024)
- Almost minimizers to a transmission problem for (p,q)-Laplacian (2024)
- Uniform Integrability in periodic homogenization of fully nonlinear elliptic equations (2023)
- Lipschitz regularity in vectorial linear transmission problems (2022)
Alla publikationer
Artiklar
- Constraint Maps with Free Boundaries (2024)
- Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems (2024)
- Almost minimizers to a transmission problem for (p,q)-Laplacian (2024)
- Uniform Integrability in periodic homogenization of fully nonlinear elliptic equations (2023)
- Lipschitz regularity in vectorial linear transmission problems (2022)
- Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations (2022)
- Nodal sets for broken quasilinear partial differential equations with Dini coefficients (2021)
- Isolated singularities for semilinear elliptic systems with power-law nonlinearity (2020)
- Higher order convergence rates in theory of homogenization II: Oscillatory initial data (2020)
- Homogenization of the boundary value for the Dirichlet problem (2019)
- Nodal sets for "broken" quasilinear pdes (2019)
- Homogenization of a Singular Perturbation Problem (2019)
- Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity (2018)
- Higher order convergence rates in theory of homogenization III: Viscous Hamilton–Jacobi equations (2018)
- An elliptic free boundary arising from the jump of conductivity (2017)
- Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form (2015)
- Constraint maps with free boundaries
- Constraint maps
- Constraint maps with free boundaries
