I am a postdoctoral researcher at the Institute for Applied Mathematics at the University of Bonn.
My research focuses on regularity theory for partial differential equations, with particular interest in nonlocal equations and kinetic equations.
I am a postdoctoral researcher at the Institute for Applied Mathematics at the University of Bonn.
My research focuses on regularity theory for partial differential equations, with particular interest in nonlocal equations and kinetic equations.
Ph. D. in Mathematics, Seoul National University, March 2020-August 2025 (Advisor: Sun-Sig Byun)
Bielefeld Seoul International Research Training Group 2235, September 2022-August 2025 (Mentor: Lars Diening)
Postdoctoral Researcher, University of Bonn, September 2025 (Mentor: Marvin Weidner)
S.-S. Byun, K. Kim, K, Song, Nonlinear nonlocal equations in Reifenberg flat domains, arXiv:2508.12595
K. Kim, H.-S. Lee, and H. Prasad, Local Hölder Regularity For Nonlocal Porous Media And Fast Diffusion Equations With General Kernel, arXiv:2504.15735.
K. Kim, H.-S. Lee, and S. Nowak, Gradient estimates for nonlinear kinetic Fokker-Planck equations, arXiv:2502.09366.
K. Kim, H.-S. Lee, and H. Prasad, Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem, to appear in SIAM J. Math. Anal.
S.-S. Byun, K. Kim, and D. Kumar, Global Calderón-Zygmund theory for fractional Laplacian type equations, J. Differential Equations (2025).
L. Diening, K. Kim, H.-S. Lee, and S. Nowak, Gradient estimates for parabolic nonlinear nonlocal equations, Calc. Var. Partial Differential Equations (2025).
L. Diening, K. Kim, H.-S. Lee, and S. Nowak, Higher differentiability for the fractional p-Laplacian, Math. Ann. (2024).
L. Diening, K. Kim, H.-S. Lee, and S. Nowak, Nonlinear nonlocal potential theory at the gradient level, J. Eur. Math. Soc (2025).
S.-S. Byun and K. Kim, L^q estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form, Commun. Contemp. Math (2025).
S.-S. Byun, K. Kim, and D. Kumar, Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci (2024).
S.-S. Byun, K. Kim, and D. Kumar, Gradient estimates for mixed local and nonlocal parabolic problems with measure data, J. Math. Anal. Appl. (2024).
S.-S. Byun and K. Kim, A Hölder estimate with an optimal tail for nonlocal parabolic p-Laplace equations, Ann. Mat. Pura Appl. (2024).
S.-S. Byun, K. Kim, and D. Kumar, Regularity results for a class of nonlocal double phase equations with VMO coefficients, Publ. Mat. (2024).
S.-S. Byun, K. Kim, and H. Kim, Higher Hölder regularity for nonlocal parabolic equations with irregular kernels, J. Evol. Equ. (2023)
email: kkim@uni-bonn.de