Postdoctoral researcher, Fakultät für Mathematik, Universität Bielefeld, Germany.
Office: V4-218
E-mail: lshnsu92@gmail.com, ho-sik.lee@uni-bielefeld.de
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1. Regularity for local and nonlocal elliptic equations
2. Calculus of variations
3. Measure data problems
Preprint
1. (with Lars Diening, Kyeongbae Kim, and Simon Nowak) Gradient estimates for parabolic nonlinear nonlocal equations, submitted.
2. (with Lars Diening, Kyeongbae Kim, and Simon Nowak) Higher differentiability for the fractional p-Laplacian, submitted.
3. (with Youchan Kim) Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities, submitted.
4. (with Sun-Sig Byun, and Kyeong Song) Regularity results for mixed local and nonlocal double phase functionals, submitted.
Published and Accepted Papers
1. (with Anna Kh. Balci) Zaremba problem with degenerate weights, Advances in Calculus of Variations, to appear.
2. (with Lars Diening, Kyeongbae Kim, and Simon Nowak) Nonlinear nonlocal potential theory at the gradient level, Journal of the European Mathematical Society, to appear.
3. (with Sun-Sig Byun, and Yumi Cho) Elliptic equations with matrix weights and measurable nonlinearities on nonsmooth domains, Proceedings of the American Mathematical Society, 152 (2024), no. 7, 2963–2982.
4. (with Sun-Sig Byun) Optimal regularity for elliptic equations with measurable nonlinearities under nonstandard growth, International Mathematics Research Notices (2024), no. 1, 423-461.
5. (with Sun-Sig Byun, and Deepak Kumar) Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities, Calculus of Variations and Partial Differential Equations 63 (2024), no. 2, Paper no. 27.
6. (with Anna Kh. Balci, Sun-Sig Byun, and Lars Diening) Global maximal regularity for equations with degenerate weights, Journal de Mathematiques Pures et Appliquees (9) 177 (2023), 484-530.
7. (with Sun-Sig Byun) Gradient estimates for non-uniformly elliptic problems with BMO nonlinearity, Journal of Mathematical Analysis and Applications 520 (2023), no. 1, Paper No. 126894, 24 pp.
8. (with Sun-Sig Byun, and Namkyeong Cho) Maximal differentiability for a general class of quasilinear elliptic equations with right-hand side measures, International Mathematics Research Notices (2022), no. 13, 9722-9754.
9. (with Sumiya Baasandorj, and Sun-Sig Byun) Gradient estimates for Orlicz double phase problems with variable exponents, Nonlinear Analysis. Theory, Methods & Applications 221 (2022), Paper No. 112891, 36 pp.
10. (with Sun-Sig Byun) Gradient estimates of ω-minimizers to double phase variational problems with variable exponents, The Quarterly Journal of Mathematics 72 (2021), no. 4, 1191–1221.
11. (with Sumiya Baasandorj, and Sun-Sig Byun) Global gradient estimates for a general class of quasilinear elliptic equations with Orlicz growth, Proceedings of the American Mathematical Society 149 (2021), no. 10, 4189–4206.
12. (with Sun-Sig Byun) Calderón-Zygmund estimates for elliptic double phase problems with variable exponents, Journal of Mathematical Analysis and Applications 501 (2021), no.1, Paper No. 124015, 31 pp.
1. Ph. D., Mathematics, Seoul National University, August 2022 (Advisor: Prof. Sun-Sig Byun)
2. Bielefeld-Seoul International Research Training Group 2235 on the graduate exchange program, September 2016-August 2022 (Mentor: Prof. Lars Diening)
1. Sep 1, 2022-Feb 28, 2023, Postdoctoral researcher, Department of Mathematical Sciences, Seoul National University, Korea. (Mentor: Prof. Sun-Sig Byun)
2. Mar 1, 2023-Present, Postdoctoral researcher, Fakultät für Mathematik, Universität Bielefeld, Germany. (Mentor: Prof. Moritz Kassmann)
