Sunghan Kim

Associate senior lecturer/Assistant Professor at Department of Mathematics; Academic staff

Telephone:
+46 18 471 31 86
E-mail:
sunghan.kim@math.uu.se
Visiting address:
Ångströmlaboratoriet, Regementsvägen 10
Postal address:
Box 480
751 06 UPPSALA

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Associate senior lecturer/Assistant Professor at Department of Mathematics; Analysis and Partial Differential Equations

Telephone:
+46 18 471 31 86
E-mail:
sunghan.kim@math.uu.se
Visiting address:
Ångströmlaboratoriet, Regementsvägen 10
Postal address:
Box 480
751 06 UPPSALA

Download contact information

CV:
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Short presentation

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

Keywords

  • analysis
  • partial differential equations
  • regularity
  • free boundary problems
  • homogenization problems
  • semilinear problems
  • parabolic pdes

Biography

My personal webpage

Research

Recently, 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: insights and related themes (with A. Figalli, A. Guerra and H. Shahgholian), La Matematica, 5 (2026), article id 26.
  • Constraint maps and free boundaries (with A. Figalli, A. Guerra and H. Shahgholian), Notices of Amer. Math. Soc, 72 (2025), 494-503.
  • Constraint maps: singularities vs free boundaries (with A. Figalli, A. Guerra and H. Shahgholian), preprint, 2024
  • Constraint maps with free boundaries: the Bernoulli case (with A. Figalli, A. Guerra and H. Shahgholian), J. Eur. Math. Soc., published online first, 2025.
  • Constraint maps with free boundaries: the obstacle case (with A. Figalli and H. Shahgholian), Arch. Ration. Mech. Anal., 248 (2024) no. 79.

Upcoming workshop: Workshop on Nonlinear PDEs, Harmonic Analysis and FBPs (Stockhom, 17-19 August, 2026)

Sunghan Kim

Publications

Recent publications

All publications

Articles in journal

Manuscripts (preprints)

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