Research

Kim, Seick. Recent Progress on second-order elliptic and parabolic equations in double divergence form.

Dong, Hongjie; Kim, Dong-ha; Kim, Seick. The Dirichlet problem for second-order elliptic equations in non-divergence form with continuous coefficients. (http://arxiv.org/abs/2402.17948)

Choi, Jongkeun; Dong, Hongjie; Kim, Dong-ha; Kim, Seick. Regularity of elliptic equations in double divergence form and applications to Green's function estimates. (http://arxiv.org/abs/2401.06621)

Kim, Seick; Sakellaris, Georgios. The Neumann Green function and scale-invariant regularity estimates for elliptic equations with Neumann data in Lipschitz domains. Calculus of Variations and Partial Differential Equations 63 (2024), no. 8, Paper No. 219, 45 pp. (doi:10.1007/s00526-024-02825-2)

Gyongy, Istvan; Kim, Seick. Harnack inequality for parabolic equations in double-divergence form with singular lower order coefficients. Journal of Differential Equations 412 (2024), 857-880. (doi:10.1016/j.jde.2024.08.070) (15 December 2024)

Dong, Hongjie; Kim, Seick; Lee, Sungjin. Note on Green's functions of non-divergence elliptic operators with continuous coefficients. Proceedings of the American Mathematical Society 151 (2023), no.5, 2045-2055. (doi:10.1090/proc/16326) (May 2023)

Dong, Hongjie; Kim, Seick; Lee, Sungjin. Estimates for fundamental solution of parabolic equations in non-divergence form. Journal of Differential Equations 340 (2022), no. 1, 557-591. (doi:10.1016/j.jde.2022.09.007) (15 December 2022)

Boullé, Nicolas; Kim, Seick; Shi, Tianyi; Townsend, Alex. Learning Green’s functions associated with time-dependent partial differential equations. Journal of Machine Learning Research 23 (2022), no. 218, 1-34. (https://jmlr.org/papers/volume23/22-0433/22-0433.pdf) (August 2022)

Kim, Seick; Xu, Longjuan. Green's function for second order parabolic equations with singular lower order coefficients. Communications on Pure and Applied Analysis 21 (2022), no. 1, 1-21. (doi:10.3934/cpaa.2021164) (January 2022)

Dong, Hongjie; Escauriaza, Luis; Kim, Seick. On C1/2,1, C1,2, and C0,0 estimates for linear parabolic operators. Journal of Evolution Equations 21 (2021), no. 4, 4641-4702. (doi:10.1007/s00028-021-00729-8) (December 2021)

Dong, Hongjie; Kim, Seick. Green's function for nondivergence elliptic operators in two dimensions. SIAM Journal on Mathematical Analysis 53 (2021), no. 4, 4637-4656. (doi:10.1137/20M1323618)

Kim, Seick; Lee, Sungjin. Estimates for Green's functions of elliptic equations in non-divergence form with continuous coefficients. Annals of Applied Mathematics 37 (2021), no. 2, 111-130. (doi:10.4208/aam.OA-2021-0001) (May 2021)

Dong, Hongjie; Kim, Seick; Lee, Jihoon. On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients. Indiana University Mathematics Journal 69 (2020), no. 6, 1815-1853. (doi:10.1512/iumj.2020.69.8028) (1 November 2020)

Choi, Jongkeun; Kim, Seick; Lee, Kyungrok. Gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients. Journal of the Korean Mathematical Society 57 (2020), no. 6, 1509-1533. (doi:10.4134/JKMS.j190777) (1 November 2020)

Hwang, Sukjung; Kim, Seick. Green's function for second order elliptic equations in non-divergence form. Potential Analysis 52 (2020), no. 1, 27-39. (doi:10.1007/s11118-018-9729-z) (January 2020)

Dong, Hongjie; Kim, Seick. Partial Schauder estimates for second-order elliptic and parabolic equations: a revisit. International Mathematics Research Notices 2019 (2019), no. 7, 2085-2136. (doi:10.1093/imrn/rnx180) (April 2019)

Kim, Seick; Sakellaris, Georgios. Green's function for second order elliptic equations with singular lower order coefficients. Communications in Partial Differential Equations 44 (2019), no. 3, 228-270. (doi:10.1080/03605302.2018.1543318) (4 March 2019)

Kim, Seick. A note on boundary blow-up problem of Δu=up, Bulletin of the Korean Mathematical Society 56 (2019), no. 1, 245-251. (doi:10.4134/BKMS.b180221) (1 January 2019)

Yoon, Gangjoon; Min, Chohong; Kim, Seick. A stable and convergent Hodge decomposition method for fluid-solid interaction. Journal of Scientific Computing 76 (2018), no. 2, 727-758. (doi:10.1007/s10915-017-0638-x) (1 August 2018)

Dong, Hongjie; Kim, Seick. Fundamental solutions for second order parabolic systems with drift terms. Proceedings of the American Mathematical Society 146 (2018), no. 7, 3019-3029. (doi:10.1090/proc/14004) (1 July 2018)

Bae, Hantaek; Kang, Kyungkeun; Kim, Seick. Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations. Journal of Differential Equations 264 (2018), no. 8, 5360-5387. (doi:10.1016/j.jde.2018.01.007) (15 April 2018)

Dong, Hongjie; Escauriaza, Luis; Kim, Seick. On C1, C2, and weak type-(1,1) estimates for linear elliptic operators: Part II. Mathematische Annalen 370 (2018), no. 1-2, 447-489. (doi:10.1007/s00208-017-1603-6) (1 February 2018)

Dong, Hongjie; Kim, Seick. On C1, C2, and weak type-(1,1) estimates for linear elliptic operators. Communications in Partial Differential Equations 42 (2017), no. 3, 417-435. (doi:10.1080/03605302.2017.1278773) (4 March 2017)

Ammari, Habib; Dong, Hongjie; Kang, Hyeonbae; Kim, Seick. On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media. International Mathematics Research Notices 2015 (2015), no. 22, 12105-12113. (doi:10.1093/imrn/rnv067) (9 March 2015)

Kim, Seick. Note on local boundedness for weak solutions of Neumann problem for second-order elliptic equations. Journal of the Korean Society for Industrial and Applied Mathematics 19 (2015), no. 2, 189-195. (doi:10.12941/jksiam.2015.19.189) (10 June 2015)

Dong, Hongjie; Kim, Seick. Regularity of a degenerate parabolic equation appearing in Vecer's unified pricing of Asian options. Bulletin of the Korean Mathematical Society 52 (2015), no. 3, 947-953. (doi:10.4134/BKMS.2015.52.3.947) (31 May 2015)

Ott, Katharine; Kim, Seick; Brown; Russell. The Green function for the mixed problem for the linear Stokes system in domains in the plane. Mathematische Nachrichten 288 (2015), no. 4, 452-464. (doi:10.1002/mana.201300281) (1 March 2015)

Choi, Jongkeun; Kim, Seick. Green's functions for elliptic and parabolic systems with Robin-type boundary conditions. Journal of Functional Analysis 267 (2014), no. 9, 3205-3261. (doi:10.1016/j.jfa.2014.08.011) (1 November 2014)

Taylor, Justin; Kim, Seick; Brown, Russell. Heat kernel for the elliptic system of linear elasticity with boundary conditions. Journal of Differential Equations 257 (2014), no. 7, 2485-2519. (doi:10.1016/j.jde.2014.05.043) (1 October 2014)

Dong, Hongjie; Kim, Seick. Green's functions for parabolic systems of second order in time-varying domains. Communications on Pure and Applied Analysis 13 (2014), no. 4, 1407-1433. (doi:10.3934/cpaa.2014.13.1407) (July 2014)

Kim, Seick; Kim, Soojung; Lee, Ki-Ahm. Harnack inequality for nondivergent parabolic operators on Riemannian manifolds. Calculus of Variations and Partial Differential Equations 49 (2014), no. 1-2, 669-706. (doi:10.1007/s00526-013-0596-6) (1 January 2014)

Choi, Jongkeun; Kim, Seick. Neumann functions for second order elliptic systems with measurable coefficients. Transactions of the American Mathematical Society 365 (2013), no. 12, 6283-6307. (doi:10.1090/S0002-9947-2013-05886-2) (1 December 2013)

Taylor, Justin; Kim, Seick; Brown, Russell. The Green function for the mixed problem for elliptic systems in two dimensions. Communications in Partial Differential Equations 38 (2013), no. 9, 1574-1600. (doi:10.1080/03605302.2013.814668) (1 September 2013)

Choi, Jongkeun; Kim, Seick. Green's function for second order parabolic systems with Neumann boundary condition. Journal of Differential Equations 254 (2013), no. 7, 2834-2860. (doi:10.1016/j.jde.2013.01.003) (1 April 2013)

Ammari, Habib; Kang, Hyeonbae; Kim, Seick. Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media. Journal of Differential Equations 253 (2012), no. 1, 41-72. (doi:10.1016/j.jde.2012.03.022) (1 July 2012)

Cho, Sungwon; Dong, Hongjie; Kim, Seick. Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains. Potential Analysis 36 (2012), no. 2, 339-372. (doi:10.1007/s11118-011-9234-0) (February 2012)

Kang, Kyungkeun; Kim, Seick. Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions. Journal of Differential Equations 251 (2011), no. 9, 2466-2493. (doi:10.1016/j.jde.2011.07.015) (1 November 2011); Corrigendum: Journal of Differential Equations 257 (2014), no. 6, 2256-2258. (doi:10.1016/j.jde.2014.05.057) (15 September 2014)

Alfonseca, M. Angeles; Auscher, Pascal; Axelsson, Andreas; Hofmann, Steve; Kim, Seick. Analyticity of layer potentials and L2 solvability of boundary value problems for divergence form elliptic equations with complex L∞ coefficients. Advances in Mathematics 226 (2011), no. 5, 4533-4606. (doi:10.1016/j.aim.2010.12.014) (20 March 2011)

Dong, Hongjie; Kim, Seick. Partial Schauder estimates for second-order elliptic and parabolic equations. Calculus of Variations and Partial Differential Equations 40 (2011), no. 3-4, 481-500. (doi:10.1007/s00526-010-0348-9) (March 2011)

Kang, Kyungkeun; Kim, Seick. Global pointwise estimates for Green's matrix of second order elliptic systems. Journal of Differential Equations 249 (2010), no. 11, 2643-2662. (doi:10.1016/j.jde.2010.05.017) (1 December 2010)

Cha, Byungchul; Kim, Seick. Biases in the prime number race of function fields. Journal of Number Theory 130 (2010), no. 4, 1048-1055. (doi:10.1016/j.jnt.2009.09.015) ( April 2010)

Dong, Hongjie; Kim, Seick. Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains. Transactions of the American Mathematical Society 361 (2009), no. 6, 3303-3323. (doi:10.1090/S0002-9947-09-04805-3) (June 2009)

Kim, Seick. On a degenerate parabolic equation arising in pricing of Asian options. Journal of Mathematical Analysis and Applications 351 (2009), no. 1, 326-333. (doi:10.1016/j.jmaa.2008.10.019) (1 March 2009)

Cho, Sungwon; Dong, Hongjie; Kim, Seick. On the Green's matrices of strongly parabolic systems of second order. Indiana University Mathematics Journal 57 (2008), no. 4, 1633-1678. (doi:10.1512/iumj.2008.57.3293) (1 August 2008)

Kim, Seick. Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients. Transactions of the American Mathematical Society 360 (2008), no. 11, 6031-6043. (doi:10.1090/S0002-9947-08-04485-1) (November 2008)

Dong, Hongjie; Kim, Seick; Safonov, Mikhail. On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equations. Communications in Partial Differential Equations 33 (2008), no. 2, 177-188. (doi:10.1080/03605300601188748) (6 February 2008)

Hofmann, Steve; Kim, Seick. The Green function estimates for strongly elliptic systems of second order. Manuscripta Mathematica 124 (2007), no. 2, 139-172. (doi:10.1007/s00229-007-0107-1) (October 2007)

Kang, Kyungkeun; Kim, Seick; Minut, Aurelia. On the regularity of solutions to a parabolic system related to Maxwell's equations. Journal of Mathematical Analysis and Applications 299 (2004), no. 1, 89-99. (doi:10.1016/j.jmaa.2004.06.009) (1 November 2004)

Hofmann, Steve; Kim, Seick. Gaussian estimates for fundamental solutions to certain parabolic systems. Publicacions Matemàtiques 48 (2004), no. 2, 481-496. (doi:10.5565/PUBLMAT_48204_10)

Kim, Seick. Harnack inequality for nondivergent elliptic operators on Riemannian manifolds. Pacific Journal of Mathematics 213 (2004), no. 2, 281-293. (doi:10.2140/pjm.2004.213.281) (February 2004)

Kang, Kyungkeun; Kim, Seick. On the Hölder continuity of solutions of a certain system related to Maxwell's equations. SIAM Journal on Mathematical Analysis 34 (2002), no. 1, 87-100 (electronic). (doi:10.1137/S0036141001393341); Erratum: SIAM Journal on Mathematical Analysis 36 (2005), no. 5, 1704-1705 (electronic). (doi:10.1137/040612907)