Welcome to Ki-Ahm Lee's Publications

Preprints:

  1. Ground State Eigenfunction for stable α-processes (with Kim, Sunghoon) (submitted)

  2. Regularity results for fully nonlinear parabolic integro-differential operators (with Kim, Yong-Cheol) (submitted)

  3. Homogenization of the boundary value for the Dirichlet Problem (with Henrik Shahgholian)(submitted)

  4. Asymptotic Behavior in Degenerate Parabolic Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems (with Kim, Soojung )(preprint)


Publications:

  1. Kim, Seick; Kim, Soojung ; Lee, Ki-Ahm Harnack inequality for nondivergent parabolic operators on Riemannian manifolds (to appear at Calculus of Variations and Partial Differential Equations)

  2. Kim, Soojung; Lee, Ki-Ahm Asymptotic Behavior in Parabolic Singular Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems (to appear at J. of Differential Equations)

  3. Lee, Ki-Ahm ; Strömqvist, Martin; Yoo, Minha Highly Oscillating Thin Obstacles (to appear at Advances in Mathematics)

  4. Choi, Sunhi ; Kim, Inwon ; Lee, Ki-Ahm Homogenization of Neumann boundary data with fully nonlinear operator (to appear at Analysis & PDE )

  5. Kim, Yong-Cheol; Lee, Ki-Ahm Hölder Regularity for fully nonlinear integro-differential operators with nonsymmetric kernels : Subcritical Case (Online First, Potential Analysis) (Journal Version)

  6. 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)

  7. 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)

  8. 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)

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

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

  11. 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)

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

  13. 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)

  14. 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)

  15. 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)

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

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

  18. 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)

  19. 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)

  20. 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)

  21. 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)

  22. 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.

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

  24. 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)

  25. 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)

  26. 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)

  27. 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)

  28. 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)

  29. 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)

  30. 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)

  31. Lee, Ki-ahm; Vázquez, 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)

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

  33. 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)

  34. 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)

  35. 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)

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