- Preprints
(with J. Ahn) Keller–Segel–Navier–Stokes systems involving general sensitivities with signal-dependent power-law decay, arXiv:2603.07870 [math.AP].
https://doi.org/10.48550/arXiv.2603.07870(with K. Kang, H. K. Kim, and J. T. Park) Existence of weak solutions for nonlinear drift-diffusion equations with measure data, arXiv:2501.07847 [math.AP].
https://doi.org/10.48550/arXiv.2501.07847- Published papers
(with K. Kang and H. K. Kim) Existence of weak solutions for fast diffusion equation with a divergence type of drift term, Nonlinear Analysis: Real World Applications, Vol. 93 (2027), 104685.
https://doi.org/10.1016/j.nonrwa.2026.104685(with K. Kang and H. K. Kim) Existence of weak solutions for porous medium equation with a divergence type of drift term in a bounded domain, Journal of Differential Equations, Vol. 389 (2024), pp. 361–414.
https://doi.org/10.1016/j.jde.2024.01.028(with K. Kang and H. K. Kim) Existence of weak solutions for porous medium equation with a divergence type of drift term, Calculus of Variations and Partial Differential Equations, Vol. 62 (2023), no. 4, Paper No. 126, 92 pp.
https://doi.org/10.1007/s00526-023-02451-4(with Y. P. Zhang) Continuity results for degenerate diffusion equations with LtpLxqL^p_t L^q_xLtpLxq drifts, Nonlinear Analysis, Vol. 211 (2021), 112413.
https://doi.org/10.1016/j.na.2021.112413(with M. Dindos and M. Mitrea) The LpL^pLp Dirichlet boundary problem for second order elliptic systems with rough coefficients, Transactions of the American Mathematical Society, Vol. 374 (2021), no. 5, pp. 3659–3701.
https://www.ams.org/journals/tran/2021-374-05/S0002-9947-2021-08306-3/(with M. Dindos and L. Dyer) Parabolic LpL^pLp Dirichlet boundary value problem and VMO-type time-varying domains, Analysis & PDE, Vol. 13 (2020), no. 4, pp. 1221–1268.
https://msp.org/apde/2020/13-4/p09.xhtml(with K. Adimurthi) Uniform boundedness for weak solutions of quasilinear parabolic equations, Proceedings of the American Mathematical Society, Vol. 148 (2020), pp. 653–665.
https://doi.org/10.1090/proc/14667(with S. Kim) Green's function for second order elliptic equations in non-divergence form, Potential Analysis, Vol. 52 (2020), pp. 27–39.
https://doi.org/10.1007/s11118-018-9729-z(with M. Dindos) The Dirichlet boundary problem for second order parabolic operators satisfying a Carleson condition, Revista Matemática Iberoamericana, Vol. 34 (2018), no. 2, pp. 767–810.
(with Y. Chung, K. Kang, and J. Kim) Hölder continuity of Keller–Segel equations of porous medium type coupled to fluid equations, Journal of Differential Equations, Vol. 263 (2017), no. 4, pp. 2157–2212.
(with G. Lieberman) Hölder continuity of bounded weak solutions to generalized parabolic ppp-Laplacian equations II: singular case, Electronic Journal of Differential Equations, Vol. 2015 (2015), no. 288, pp. 1–24.
(with G. Lieberman) Hölder continuity of bounded weak solutions to generalized parabolic ppp-Laplacian equations I: degenerate case, Electronic Journal of Differential Equations, Vol. 2015 (2015), no. 287, pp. 1–32.
- Theses
Hölder regularity of solutions of generalized ppp-Laplacian type parabolic equations, Doctoral thesis, Iowa State University, 2012.
http://lib.dr.iastate.edu/etd/12667Support vector machine via semidefinite and second order cone programming relaxation methods, Master's thesis, South Korea National Assembly Library, 2007.