Welcome to Ki-Ahm Lee's Publications



Publications:

  1. Moritz Kassmann, Minhyun Kim, Ki-Ahm Lee; Robust near-diagonal Green function estimates ( to appear at IMRN)

  2. Kim, Minhyun; Lee, Ki-Ahm; Lee, Se-Chan; The Wiener Criterion for Nonlocal Dirichlet Problems Communications in Mathematical Physics (2023) (Journal Version)

  3. Kim, Takwon; Lee, Ki-Ahm; Park, Jinwan; A double obstacle problem in an optimal investment problem. Nonlinear Anal. 232 (2023), Paper No. 113282. (Journal Version)

  4. Lee, Ki-Ahm; Park, Sungha Non-linear operators of divergence form on the Sierpinski gasket. Nonlinear Anal. 232 (2023), Paper No. 113256. (Journal Version)

  5. Kim, Inyoung; Kim, Takwon; Lee, Ki-Ahm; Yoon, Ji-Hun; New approach and analysis of the generalized constant elasticity of variance model. Appl. Stoch. Models Bus. Ind. 39 (2023), no. 1, 114-155. (Journal Version)

  6. Kim, Takwon; Lee, Ki-Ahm; Yun, Hyungsung; Higher regularity up to boundary for degenerate parabolic equations. J. Differential Equations 348 (2023), 223-277. (Journal Version)

  7. Lee, Ki-Ahm; Lee, Se-Chan; Viscosity method for random homogenization of fully nonlinear elliptic equations with highly oscillating obstacles. Adv. Nonlinear Anal. 12 (2023), no. 1, 266-303. (Journal Version)

  8. Kim, Sunghoon; Lee, Ki-Ahm; Properties of generalized degenerate parabolic systems. Adv. Nonlinear Anal. 11 (2022), no. 1, 1048-1084. (Journal Version)

  9. Kim, Sunghan; Lee, Ki-Ahm; Uniform estimates in periodic homogenization of fully nonlinear elliptic equations. Arch. Ration. Mech. Anal. 243 (2022), no. 2, 697-745. (Journal Version)

  10. Kim, Jongmyeong; Kim, Minhyun; Lee, Ki-Ahm Harnack inequality for nonlocal operators on manifolds with nonnegative curvature. Calc. Var. Partial Differential Equations 61 (2022), no. 1, Paper No. 22, 29 pp. (Journal Version)

  11. Lee, Ki-Ahm; Lee, Taehun; Park, Jinwan The obstacle problem for parabolic Monge-Ampére equation. J. Differential Equations 309 (2022), 608 - 649. (Journal Version)

  12. Lee, Ki-Ahm; Park, Jinwan; The regularity theory for the parabolic double obstacle problem. Math. Ann. 381 (2021), no. 1-2, 685-728. (Journal Version)

  13. Lee, Ki-Ahm; Lee, Taehun; Gauss curvature flow with an obstacle. Calc. Var. Partial Differential Equations 60 (2021), no. 5, Paper No. 166, 23 pp. (Journal Version)

  14. Lee, Ki-Ahm; Lee, Se-Chan; The Wiener criterion for elliptic equations with Orlicz growth. J. Differential Equations 292 (2021), 132-175. (Journal Version)

  15. Lee, Ki-Ahm; Lee, Taehun; Park, Jinwan; The obstacle problem for the Monge-Ampére equation with the lower obstacle. Nonlinear Anal. 210 (2021), Paper No. 112374, 23 pp. (Journal Version)

  16. Choi, Kyeongsu; Daskalopoulos,Panagiota; Lee, Ki-Ahm Translating solutions to the Gauss curvature flow with flat sides Anal. PDE 14 (2021), no. 2, 595-616. (Journal Version)

  17. González, María del Mar; Lee, Ki-Ahm; Lee, Taehun; Optimal configuration and symmetry breaking phenomena in the composite membrane problem with fractional Laplacian. J. Differential Equations 274 (2021), 1165-1208. (Journal Version)

  18. Kim, Sunghoon; Lee, Ki-Ahm System of porous medium equations. J. Differential Equations 272 (2021), 433-472. (Journal Version)

  19. Kim, Minhyun; Lee, Ki-Ahm; Generalized Evans-Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders. J. Differential Equations 270 (2021), 883-915. (Journal Version)

  20. Sun, Peng; Kim, Inyoung; Lee, Kiahm; Flexible weighted Dirichlet process mixture modelling and evaluation to address the problem of forecasting return distribution. J. Nonparametr. Stat. 32 (2020), no. 4, 989-1014. (Journal Version)

  21. Kim, Minhyun; Lee, Ki-Ahm Regularity for fully nonlinear integro-differential operators with kernels of variable orders Nonlinear Anal. 193 (2020), 111312. (Journal Version)

  22. Kang, Hyunsuk ; Kim, Lami ; Lee, Ki-Ahm Anisotropic flow of convex hypersurfaces by the square root of the scalar curvature (Journal Version)

  23. Kim, Sunghan; Lee, Ki-Ahm Higher Order Convergence Rates in Theory of Homogenization II: Oscillatory Initial Data Adv. Math. 362 (2020) 106960 (Journal Version)

  24. Kim, Sunghoon; Lee, Ki-Ahm Local Continuity and Asymptotic Behaviour of Degenerate Parabolic Systems Nonlinear Anal. 192 (2020), 111702. (Journal Version)

  25. Choi, Kyeongsu; Daskalopoulos, Panagiota; Kim, Lami; Lee, Ki-ahm The evolution of complete non-compact graphs by powers of Gauss curvature J. Reine Angew. Math. 757 (2019), 131-158 (Journal Version)

  26. Lee, Ki-Ahm; Lee, Kiseop; Park, Sang-Hyeon A financial market of a stochastic delay equation. Bull. Korean Math. Soc. 56 (2019), no. 5, 1129-1141.

  27. Kim, Minhyun; Kim, Panki; Lee, Jaehun; Lee, Ki-Ahm Boundary regularity for nonlocal operators with kernels of variable orders J. Funct. Anal. 277 (2019), no. 1, 279-332.

    (Journal Version)

  28. Byun,Sun-sig; Lee, Ki-ahm; Oh, Jehan; Park, Jinwan Regularity Results of the Thin Obstacle Problem for the p(x)-Laplacian J. Funct. Anal. 276 (2019), no. 2, 496-519 (Journal Version)

  29. Lee, Ki-ahm; Park, Jinwan; Shahgholian, Henrik The Regularity Theory for the Double Obstacle Problem Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 104, 19 pp.

  30. Kim, Sunghan; Lee, Ki-Ahm;Shahgholian, Henrik Nodal Sets for "Broken" Quasilinear PDEs Indiana Univ. Math. J. 68 (2019), no. 4, 1113-1148.

  31. Byun, Sun-Sig; Lee, Ki-Ahm; Oh, Jehan; Park, Jinwan Nondivergence elliptic and parabolic problems with irregular obstacles Math. Z. 290 (2018), no. 3-4, 973-990 (Journal Version)

  32. Lee, Ki-ahm; Park, Jinwan Obstacle Problem for a Non-convex Fully Nonlinear operator J. Differential Equations 265 (2018), no. 11, 5809-5830

  33. Kim, Sunghan; Lee, Ki-Ahm Higher Order Convergence Rates in Theory of Homogenization III: viscous Hamilton-Jacobi Equations J. Differential Equations 265 (2018), no. 10, 5384-5418. (Journal Version)

  34. Kang, Hyunsuk; Lee, Ki-Ahm; Harnack inequality and pinching estimates for anisotropic curvature flow of hypersurfaces. J. Math. Anal. Appl. 464 (2018), no. 1, 32-57. (Journal Version)

  35. Chae, Myeongju; Kang, Kyungkeun; Lee, Jihoon; Lee, Ki-Ahm A regularity condition and temporal asymptotics for chemotaxis-fluid equations. Nonlinearity 31 (2018), no. 2, 351-387. (Journal Version)

  36. Sun, Peng; Kim, Inyoung; Lee, Ki-Ahm Dual-semiparametric regression using weighted Dirichlet process mixture. Comput. Statist. Data Anal. 117 (2018), 162-181. (Journal Version)

  37. Choi, Jongkeun; Lee, Ki-Ahm The Green function for the Stokes system with measurable coefficients. Commun. Pure Appl. Anal. 16 (2017), no. 6, 1989-2022 (Journal Version)

  38. Kim, Sunghan; Lee, Ki-Ahm; Shahgholian, Henrik An elliptic free boundary arising from the jump of conductivity. Nonlinear Anal. 161 (2017), 1-29. (Journal Version)

  39. Kim, Yong-Cheol; Lee, Ki-Ahm The The Evans-Krylov theorem for nonlocal parabolic fully nonlinear equations Nonlinear Anal. 160 (2017), 79-107 (Journal Version)

  40. Choi, Woocheol; Kim, Seunghyeok; Lee, Ki-Ahm Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents. Adv. Math. 298 (2016), 484-533. (Journal Version)

  41. Kim, Soojung; Kim, Yong-Cheol; Lee, Ki-Ahm Regularity for fully nonlinear integro-differential operators with regularly varying kernels. Potential Anal. 44 (2016), no. 4, 673-705. (Journal Version)

  42. Kim, Sunghoon; Lee, Ki-Ahm Hölder regularity and uniqueness theorem on weak solutions to the degenerate Keller-Segel system. Nonlinear Anal. 138 (2016), (Journal Version)

  43. Kim, Sunghan; Lee, Ki-Ahm Higher order convergence rates in theory of homogenization: equations of non-divergence form. Arch. Ration. Mech. Anal. 219 (2016), no. 3, 1273-1304 (Journal Version)

  44. Kim, Yong-Cheol; Lee, Ki-Ahm Cordes-Nirenberg type estimates for nonlocal parabolic equations. Nonlinear Anal. 130 (2016), 330-360. (Journal Version)

  45. Lee, Ki-Ahm Homogenization theory in nonlinear partial differential equations. Proceedings of the International Congress of Mathematicians-Seoul 2014. Vol. III, 811-834, Kyung Moon Sa, Seoul, 2014.

  46. Soojung Kim; Ki-Ahm Lee Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds J. Funct. Anal. 267 (2014), no. 7, 2152-2198 (Journal Version)

  47. Woocheol Choi; Seunghyeok Kim; Ki-Ahm Lee Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian J. Funct. Anal. 266 (2014), no. 11, 6531-6598 (Journal Version)

  48. Sunghoon Kim; Ki-Ahm Lee Geometric Properties of Gelfand's Problems with Parabolic Approach J. Math. Anal. Appl. 414 (2014), no. 2, 978-995. (Journal Version)

  49. Kim, Seick; Kim, Soojung ; Lee, Ki-Ahm Harnack inequality for nondivergent parabolic operators on Riemannian manifolds Calc. Var. Partial Differential Equations 49 (2014), no. 1-2, 669-706 (Journal Version)

  50. Kim, Yong-Cheol; Lee, Ki-Ahm Regularity results for fully nonlinear parabolic integro-differential operators Math. Ann. 357 (2013), no. 4, 1541-1576 (Journal Version)

  51. Lee, Ki-Ahm ; Strömqvist, Martin; Yoo, Minha Highly Oscillating Thin Obstacles Advances in Mathematics, Vol 237, nb. 1 (2013), 286-315 (Journal Version)

  52. Choi, Sunhi ; Kim, Inwon ; Lee, Ki-Ahm Homogenization of Neumann boundary data with fully nonlinear operator Analysis & PDE , Vol. 6 (2013), No. 4, 951-972 (Journal Version)

  53. Kim, Soojung; Lee, Ki-Ahm Asymptotic Behavior in Parabolic Singular Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems J. of Differential Equations Vol 254, Issue 8 ( 2013) p 3259 - 3306 (Journal Version)

  54. Kim, Yong-Cheol; Lee, Ki-Ahm Hölder Regularity for fully nonlinear integro-differential operators with nonsymmetric kernels : Subcritical Case Potential Analysis Vol 38, Issue 2 (2013), pp 433-455 (Journal Version)

  55. Kim, Lami ; Lee, Ki-Ahm; Rhee, Eunjai α-Gauss Curvature Flows with Flat Sides J. of Differential Equations Vol. 254, no 3, (2013), 1172-1192 (Journal Version)

  56. Kim, Yong-Cheol; Lee, Ki-Ahm Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels MANUSCRIPTA MATHEMATICA Vol. 139, no 3-4 (2012), 291-319 (Journal Version)

  57. Lee, Ki-Ahm ; Yoo, Minha Viscosity Method for Homogenization of Fully Nonlinear Equations with Neumann data in Perforated Domains Arkiv for Rational Mechanics and Analysis, Volume 206, Number 1 (2012), 297-332 (Journal Version)

  58. Daskalopoulos, P; Lee, Ki-Ahm Fully Degenerate Monge Ampére Equations J. of Differential Equations Vol 253 no. 6, (2012), 1665-1691 (Journal Version)

  59. Lee, Ki-Ahm; Rhee, Eunjai Rolling Stones with nonconvex sides I: Regularity theory J. Korean Math. Soc. (2012) 49:265-291. (Journal Version)

  60. Lee, Ki-Ahm; Rhee, Eunjai Rolling Stones with nonconvex sides II: All time regularity of Interface and surface J. Korean Math. Soc. (2012) 49:585-604. (Journal Version)

  61. Kim, Sunghoon.; Lee, Ki-Ahm Hölder Estimates for Singular Non-local Parabolic Equations Journal of Functional Analysis ,261, (2011) 3482- 3518. (Journal Version)

  62. Kim, Sunghoon.; Lee, Ki-Ahm Viscosity method for Homogenization of Parabolic Nonlinear Equations in Perforated Domains J. Differential Equations, 251, (2011) 2296-2326. (Journal Version)

  63. Kim, Sunghoon; Lee, Ki-Ahm Smooth solution for the porous medium equation in a bounded domain. J. Differential Equations 247 (2009), no. 4, 1064--1095. (Journal Version)

  64. Ki-Ahm Lee Geometric Properties in Parabolic Flows and its Applications Problems in the Calculus of Variational and Related Topics, RIMS proceedings 1628 (2009), 71-86 (Journal Version)

  65. Lee, Ki-Ahm; Vazquez, J.L. Parabolic approach to Nonlinear Elliptic Eigenvalue Problems. Advances in Mathematics 219 (2008) no. 6, 2006-2028 (Journal Version)

  66. Caffarelli, L.; Lee, K. Viscosity Method in Homogenization of Highly Oscillating Obstacles Indiana Univ. Math. J. 57 (2008), no. 4, 1715--1741 (Journal Version)

  67. Caffarelli, L.; Lee, K. Homogenization of oscillating free boundaries: the elliptic case. Comm. Partial Differential Equations 32 (2007), no. 1-3, 149--162. (Journal Version)

  68. Caffarelli, L. A.; Lee, K.-A.; Mellet, A. Flame propagation in one-dimensional stationary ergodic media. Math. Models Methods Appl. Sci. 17 (2007), no. 1, 155--169. (Journal Version)

  69. Lee, Ki-ahm; Petrosyan, Arshak; Vazquez, Juan Luis Large-time geometric properties of solutions of the evolution p-Laplacian equation. J. Differential Equations 229 (2006), no. 2, 389--411. (Journal Version)

  70. Caffarelli, L.;Lee, Ki-Ahm; Mellet, A. Homogenization and flame propagation in periodic excitable media: The asymptotic speed of Propagation Comm. Pure Appl. Math. 59 (2006), no. 4, 501--525. (Journal Version)

  71. Caffarelli, L.; Lee, Ki-Ahm Homogenization of nonvariational viscosity solutions. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 29 (2005), no. 1, 89--100.

  72. Lee, Ki-Ahm; The power-concavity on nonlinear parabolic flows Comm. Pure Appl. Math. 58 (2005), no. 11, 1529--1543. (Journal Version)

  73. Caffarelli, L.;Lee, Ki-Ahm; Mellet, A. Singular limit and homogenization for flame propagation in periodic excitable media ( Archive for Rational Mechanics and Analysis, 172(2004),no2, 153-190) (Journal Version)

  74. Daskalopoulos, P; Lee, Ki-Ahm All time smooth solutions of the one-phase Stefan problem and the Hele-Shaw flow (Communications on Partial Differential Equations,29 (2004), no. 1-2, 71--89.) (Journal Version)

  75. Daskalopoulos, P; Lee, Ki-Ahm Worn Stones with Flat Sides The Regularity of the Interface ( Invent. Math,156 (2004), no. 3, 445--493) (Journal Version)

  76. Lee, Ki-Ahm; Shahgholian, Henrik Hausdorff dimension and stability for the p-Obstacle problem (2< p < ∞) (Journal of Differential Equations,195 (2003), no. 1, 14--24.) (Journal Version)

  77. Lee, Ki-Ahm; Vazquez, J. L. Geometrical properties of solutions of the Porous Medium Equation for large times (Indiana Mathematics Journal,52 (2003), no. 4, 991--1016) (Journal Version)

  78. Daskalopoulos, P; Lee, Ki-Ahm Hölder Regularity of Solutions to Degenerate Elliptic and Parabolic Equations ( Functional Analysis Vol 201, Issue 2 (2003)341-379) (Journal Version)

  79. Daskalopoulos, P; Lee, Ki-Ahm All time existence of a smooth solution for the one-phase free boundary problem of the flame type (Comm. Pure Appl. Math. 55 (2002), no. 5, 633--653) (Journal Version)

  80. Lee, Ki-ahm; Vazquez, J. L. Geometrical properties of solutions of the porous medium equation for large times.}XVII CEDYA: Congress on Differential Equations and Applications/VII CMA: Congress on Applied Mathematics (Spanish) (Salamanca, 2001), 221-244, Dep. Mat. Apl., Univ. Salamanca, Salamanca, 2001. (Journal Version)

  81. Lee, Ki-ahm The Obstacle Problem for Monge-Ampére Equation (Comm. in P.D.E. Volume 26, 1&2.,33-42,2001) (Journal Version)

  82. Lee, Ki-Ahm; Shahgholian, Henrik Regularity of a free boundary for viscosity solutions of nonlinear elliptic equations (Comm. Pure Appl. Math. 54 (2001), no. 1, 43--56) (Journal Version)

  83. Daskalopoulos, P; Lee, Ki-Ahm Free-Boundary Regularity on the Focusing Problem for the Gauss Curvature Flow with Flat Sides ( Math. Z. 237 (2001), no. 4, 847--874) (Journal Version)

  84. Daskalopoulos, P;Hamilton, R.; Lee, Ki-Ahm All time C∞-Regularity of interface in degenerated diffusion: a geometric approach (Duke Mathematical Journal Vol 108, No.2, 295-327, 2001 ) (Journal Version)

  85. Lee, Ki-Ahm Obstacle Problem for Nonlinear 2nd-Order Elliptic Operator (Ph-Thesis, New York University, 1998)