Minhyun Kim

Preprints

Liouville theorem for singular solutions to nonlocal equations (with Se-Chan Lee), arXiv:2507.09587, 25 pp.
Semiregular and strongly irregular boundary points for nonlocal Dirichlet problems (with Anders Björn and Jana Björn), arXiv:2506.23188, 23 pp.
Removable singularities for nonlocal minimal graphs, arXiv:2501.14299, 16 pp.
Singularities of solutions of nonlocal nonlinear equations (with Se-Chan Lee), arXiv:2410.13292, 38 pp.
Optimal boundary regularity and Green function estimates for nonlocal equations in divergence form (with Marvin Weidner), arXiv:2408.12987, 57 pp.
Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems (with Anders Björn and Jana Björn), arXiv:2406.05994, 33 pp.
Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth (with Se-Chan Lee), arXiv:2311.01246, 42 pp.
Gradient Riesz potential estimates for a general class of measure data quasilinear systems (with Iwona Chlebicka and Marvin Weidner), arXiv:2307.15525, 36 pp.
The fractional p-Laplacian on hyperbolic spaces (with Jongmyeong Kim and Ki-Ahm Lee), arXiv:2210.07029, 23 pp.
Harnack inequality for fractional Laplacian-type operators on hyperbolic spaces (with Jongmyeong Kim and Ki-Ahm Lee), arXiv:2108.08746, 44 pp.

Publications

Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth (with Ki-Ahm Lee and Se-Chan Lee)
J. Funct. Anal. 288 (2025), no. 1, Paper No. 110690, 51 pp.
Curvature bound for Lₚ Minkowski problem (with Kyeongsu Choi and Taehun Lee)
Adv. in Math. 458 (2024), Paper No. 109959, 31 pp.
Diameter estimate for planar Lₚ dual Minkowski problem (with Taehun Lee)
Proc. Amer. Math. Soc. 152 (2024), no. 7, 3035–3049.
Robust near-diagonal Green function estimates (with Moritz Kassmann and Ki-Ahm Lee)
Int. Math. Res. Not. IMRN 2023, no. 19, 16957–16993.
Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents
Ann. Mat. Pura Appl. (4) 202 (2023), no. 6, 2653–2664.
Local regularity for nonlocal equations with variable exponents (with Jamil Chaker)
Math. Nachr. 296 (2023), no. 9, 4463–4489.
The Wiener criterion for nonlocal Dirichlet problems (with Ki-Ahm Lee and Se-Chan Lee)
Comm. Math. Phys. 400 (2023), no. 3, 1961–2003.
Harnack inequality for nonlocal problems with non-standard growth (with Jamil Chaker and Marvin Weidner)
Math. Ann. 386 (2023), no. 1-2, 533–550.
The concentration-compactness principle for the nonlocal anisotropic p-Laplacian of mixed order (with Jamil Chaker and Marvin Weidner)
Nonlinear Anal. 232 (2023), Paper No. 113254, 18 pp.
Regularity for nonlocal problems with non-standard growth (with Jamil Chaker and Marvin Weidner)
Calc. Var. Partial Differential Equations 61 (2022), no. 6, Paper No. 227, 31 pp.
Regularity estimates for fractional orthotropic p-Laplacians of mixed order (with Jamil Chaker)
Adv. in Nonlinear Anal. 11 (2022), no. 1, 1307–1331.
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature (with Jongmyeong Kim and Ki-Ahm Lee)
Calc. Var. Partial Differential Equations 61 (2022), no. 1, Paper No. 22, 29 pp.
Generalized Evans–Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders (with Ki-Ahm Lee)
J. Differential Equations 270 (2021), 883–915.
Regularity for fully nonlinear integro-differential operators with kernels of variable orders (with Ki-Ahm Lee)
Nonlinear Anal. 193 (2020), 111312, 27 pp.
Boundary regularity for nonlocal operators with kernels of variable orders (with Panki Kim, Jaehun Lee and Ki-Ahm Lee)
J. Funct. Anal. 277 (2019), no. 1, 279–332.

Ph.D. Thesis

Regularity theory for nonlocal operators, Seoul National University, 2020.

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