{"id":70,"date":"2017-04-27T14:45:01","date_gmt":"2017-04-27T05:45:01","guid":{"rendered":"http:\/\/192.168.99.111\/dkim\/?page_id=70"},"modified":"2025-11-19T16:21:55","modified_gmt":"2025-11-19T07:21:55","slug":"my-publications","status":"publish","type":"page","link":"https:\/\/mathematicians.korea.ac.kr\/dkim\/my-publications\/","title":{"rendered":"My Publications"},"content":{"rendered":"
Submitted<\/strong><\/h5>\n
    \n
  1. Doyoon Kim and Junbin Song. Trace Regularity PINNs: Enforcing \"\mathrm{H}^{\frac{1}{2}}(\partial \Omega)\" for Boundary Data.<\/a> Submitted.<\/li>\n
  2. Hongjie Dong, Pilgyu Jung, and Doyoon Kim. \"L_p\"-estimates of the conormal derivative problem for parabolic equations with time measurable coefficients and \"A_p\"-weights.<\/a> Submitted.<\/li>\n<\/ol>\n
    Published<\/h5>\n
      \n
    1. Pilgyu Jung and Doyoon Kim. \"L_p\"-estimates for parabolic equations in divergence form with a half-time derivative.<\/a> (https:\/\/authors.elsevier.com\/a\/1lH0Z_W4cPkNh<\/a>) JDE, 443 (<\/span><\/span>2025), 113560.<\/li>\n
    2. Doyoon Kim and Kwan Woo. Sobolev spaces and trace theorems for time-fractional evolution equations.<\/a> Potential Analysis, 63 (2025), 1289–1333.<\/li>\n
    3. Jongkeun Choi and Doyoon Kim. Green functions for stationary Stokes systems with conormal derivative boundary condition in two dimensions.<\/a> Mathematische Nachrichten, 297 (2024), no.5, 1712–1736.<\/li>\n
    4. Doyoon Kim, Kyeong-Hun Kim, and Kwan Woo. Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces.<\/a> Stochastics and Partial Differential Equations: Analysis and Computations, , 12 (2024), no.1, 134–172.<\/li>\n
    5. Hongjie Dong and Doyoon Kim. Time fractional parabolic equations with partially SMO coefficients.<\/a> JDE, 377 (2023), 759–808.<\/li>\n
    6. Hongjie Dong, Pilgyu Jung, and Doyoon Kim. Boundedness of non-local operators with spatially dependent coefficients and \"L_p\"-estimates for non-local equations.<\/a> CVPDE, 62 (2023), no.2, Paper No.62, 28 pp.<\/li>\n
    7. Hongjie Dong, Doyoon Kim, and Tuoc Phan. Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients.<\/a> CPDE, 47 (2022), no.8, 1700–1731.<\/li>\n
    8. Doyoon Kim, Kyeong-Hun Kim, and Kijung Lee. Parabolic systems with measurable coefficients in weighted Sobolev spaces.<\/a> CPAA, 21 (2022), no.8, 2587–2613.<\/li>\n
    9. Doyoon Kim, Seungjin Ryu, and Kwan Woo. Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms.<\/a> J. Evol. Equ., 22 (2022). no.1, Paper No.9, 40 pp.<\/li>\n
    10. Hongjie Dong and Doyoon Kim. Time fractional parabolic equations with measurable coefficients and embeddings for fractional parabolic Sobolev spaces.<\/a> IMRN, 2021 (2021), no.22, 17563–17610.<\/li>\n
    11. Hongjie Dong and Doyoon Kim. An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives.<\/a> Adv. Math., 377 (2021), Paper No.107494, 44 pp.<\/li>\n
    12. Hongjie Dong and Doyoon Kim. \"L_p\"-estimates for time fractional parabolic equations in divergence form with measurable coefficients.<\/a> JFA, 278 (2020), no.3, 108338, 66 pp.<\/li>\n
    13. Doyoon Kim and Seungjin Ryu. The weak maximum principle for second-order elliptic and parabolic conormal derivative problems.<\/a> CPAA, 19 (2020), no.1, 493–510.<\/li>\n
    14. Hongjie Dong and Doyoon Kim. \"L_q\"-estimates for stationary Stokes system with coefficients measurable in one direction.<\/a> (http:\/\/rdcu.be\/GCJ1<\/a>) Bull. Math. Sci., 9 (2019), no.1, 1950004, 30 pp.<\/li>\n
    15. Jongkeun Choi and Doyoon Kim. Weighted \"L_{p,q}\"-estimates for higher order elliptic and parabolic systems with BMO\"_x\" coefficients on Reifenberg flat domains.<\/a> (https:\/\/rdcu.be\/bAY4C<\/a>) CVPDE, 58 (2019), no.3, Paper No.90, 29 pp.<\/li>\n
    16. Jongkeun Choi and Doyoon Kim. Estimates for Green functions of Stokes systems in two dimensional domains.<\/a> J. Math. Anal. Appl., 471 (2019), no.1-2, 102–125.<\/li>\n
    17. Hongjie Dong and Doyoon Kim. \"L_p\"-estimates for time fractional parabolic equations with coefficients measurable in time.<\/a> Adv. Math., 345 (2019), 289–345.<\/li>\n
    18. Jongkeun Choi, Hongjie Dong, and Doyoon Kim. Green functions of conormal derivative problems for stationary Stokes system.<\/a> (https:\/\/rdcu.be\/3b1D<\/a>) J. Math. Fluid Mech., 20 (2018), no.4, 1745–1769.<\/li>\n
    19. Hongjie Dong and Doyoon Kim. On \"L_p\"-estimates for elliptic and parabolic equations with \"A_p\" weights.<\/a> Trans. Amer. Math. Soc., 370 (2018), no.7, 5081–5130.<\/li>\n
    20. Jongkeun Choi, Hongjie Dong, and Doyoon Kim. Conormal derivative problems for stationary Stokes system in Sobolev spaces.<\/a> DCDS-A, 38 (2018), no.5, 2349–2374.<\/li>\n
    21. Hongjie Dong and Doyoon Kim. Weighted \"L_q\"-estimates for stationary Stokes system with partially BMO coefficients.<\/a> JDE, 264 (2018), no.7, 4603–4649.<\/li>\n
    22. Doyoon Kim, Hongjie Dong, and Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO\"_x\" coefficients in weighted Sobolev spaces.<\/a> DCDS-A, 36 (2016), no.9, 4895–4914.<\/li>\n
    23. Sungwon Cho, Hongjie Dong, and Doyoon Kim. Boundary value problems for parabolic operators in a time-varying domain.<\/a> CPDE, 40 (2015), no.7, 1282–1313.<\/li>\n
    24. Hongjie Dong and Doyoon Kim. Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces.<\/a> Adv. Math., 274 (2015), 681–735.<\/li>\n
    25. Hongjie Dong and Doyoon Kim. On the impossibility of \"W_p^2\" estimates for elliptic equations with piecewise constant coefficients.<\/a> JFA, 267 (2014), no.10, 3963–3974.<\/li>\n
    26. Hongjie Dong and Doyoon Kim. Parabolic equations in simple convex polytopes with time irregular coefficients.<\/a> SIAM J. Math. Anal., 46 (2014), no.3, 1789–1819.<\/li>\n
    27. Hongjie Dong and Doyoon Kim. Schauder estimates for a class of non-local elliptic equations.<\/a> DCDS-A, 33 (2013), no.6, 2319–2347.<\/li>\n
    28. Hongjie Dong and Doyoon Kim. The conormal derivative problem for higher order elliptic systems with irregular coefficients.<\/a> in Recent Advances in Harmonic Analysis and Partial Differential Equations, Contemporary Mathematics, vol. 581, Amer. Math. Soc., Providence, RI, 2012, pp. 69–97.<\/li>\n
    29. Doyoon Kim. Global regularity of solutions to quasiliner conormal derivative problem with controlled growth.<\/a> J. Korean Math. Soc., 49 (2012), No.6, 1273–1299.<\/li>\n
    30. Hongjie Dong and Doyoon Kim. On \"L_p\"-estimates for a class of non-local elliptic equations.<\/a> JFA, 262 (2012), no.3, 1166–1199.<\/li>\n
    31. Hongjie Dong and Doyoon Kim. Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controllable growth.<\/a> CPDE, 36 (2011), no.10, 1750–1777.<\/li>\n
    32. Hongjie Dong and Doyoon Kim. Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains.<\/a> JFA, 261 (2011), no.11, 3279–3327.<\/li>\n
    33. Hongjie Dong and Doyoon Kim. Parabolic and elliptic systems in divergence form with variably partially BMO coefficients.<\/a> SIAM J. Math. Anal., 43 (2011), no.3, 1075–1098.<\/li>\n
    34. Hongjie Dong and Doyoon Kim. On the \"L_p\"-solvability of higher order parabolic and elliptic systems with BMO coefficients.<\/a> Arch. Ration. Mech. Anal., 199 (2011), no.3, 889–941.<\/li>\n
    35. Hongjie Dong and Doyoon Kim. \"L_p\" solvability of divergence type parabolic and elliptic systems with partially BMO coefficients.<\/a> CVPDE, 40 (2011), no.3-4, 357–389.<\/li>\n
    36. Doyoon Kim. Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms.<\/a> Potential Analysis, 33 (2010), no.1, 17–46.<\/li>\n
    37. Hongjie Dong and Doyoon Kim. Elliptic equations in divergence form with partially BMO coefficients.<\/a> Arch. Ration. Mech. Anal., 196 (2010), no.1, 25–70.<\/li>\n
    38. Hongjie Dong and Doyoon Kim. Parabolic and elliptic systems with VMO coefficients.<\/a> Methods Appl. Anal., 16 (2009), no.3, 365–388.<\/li>\n
    39. Doyoon Kim. Elliptic and parabolic equations with measurable coefficients in \"L_p\"-spaces with mixed norms.<\/a> Methods Appl. Anal., 15 (2008), no.4, 437–468.<\/li>\n
    40. R.M. Balan and Doyoon Kim. The stochastic heat equation driven by a Gaussian noise: Markov property.<\/a> Commun. Stoch. Anal., 2 (2008), no.2, 229–249.<\/li>\n
    41. Doyoon Kim. Elliptic equations with nonzero boundary conditions in weighted Sobolev spaces.<\/a> J. Math. Anal. Appl., 337 (2008), no.2, 1465–1479.<\/li>\n
    42. Doyoon Kim. Trace theorems for Sobolev-Slobodeckij spaces with or without weights.<\/a> J. Funct. Spaces Appl., 5 (2007), no.3, 243–268.<\/li>\n
    43. Doyoon Kim. Parabolic equations with measurable coefficients II.<\/a> J. Math. Anal. Appl., 334 (2007), no.1, 534–548.<\/li>\n
    44. Doyoon Kim and N.V. Krylov. Parabolic equations with measurable coefficients.<\/a> Potential Analysis, 26 (2007), no.4, 345–361.<\/li>\n
    45. Doyoon Kim and N.V. Krylov. Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others.<\/a> SIAM J. Math. Anal., 39 (2007), no.2, 489–506.<\/li>\n
    46. Doyoon Kim. Second order elliptic equations in \"\mathbb{R}^{d}\" with piecewise continuous coefficients.<\/a> Potential Analysis, 26 (2007), no.2, 189–212.<\/li>\n
    47. Doyoon Kim. Second order parabolic equations and weak uniqueness of diffusions with discontinuous coefficients.<\/a> Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 5 (2006), no.1, 55–76.<\/li>\n
    48. Doyoon Kim. Partial differential equations in Sobolev spaces with or without weights. PhD thesis, University of Minnesota, 2005.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      Submitted Doyoon Kim and Junbin Song. Trace Regularity PINNs: Enforcing for Boundary Data. Submitted. Hongjie Dong, Pilgyu Jung, and Doyoon Kim. -estimates of the conormal derivative problem for parabolic equations with time measurable coefficients and -weights. Submitted. Published Pilgyu Jung<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-70","page","type-page","status-publish","hentry"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"Homepage for Doyoon Kim","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/dkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/pages\/70","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/comments?post=70"}],"version-history":[{"count":87,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/pages\/70\/revisions"}],"predecessor-version":[{"id":234,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/pages\/70\/revisions\/234"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/media?parent=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}