Publications

Publications

1. J.-H. Choi, I.Kim, A maximal Lp-regularity theory to initial value problems with time measurable nonlocal operators generated by additive processes. Stochastics and Partial Differential Equations: Analysis and Computations, Volume 12, Issue 1, pages 352-415, 2024. [arXiv link 47 pages, Journal link 64 pages]

2. J.-H. Choi, J. Kang, D. Park, A regularity theory for parabolic equations with anisotropic non-local operators in Lq(Lp) spaces. SIAM Journal on Mathematical Analysis, Volume 56, No. 1, pages 1264-1299, 2024. [arXiv link 31 pages, Journal link 36 pages]

3. J.-H. Choi, I.Kim,  A weighted Lp-regularity theory for parabolic partial differential equations with time measurable pseudo-differential operators. Journal of Pseudo-Differential Operators and Applications, Volume 14, Issue 4, Article no.55, 2023. [arXiv link 41 pages, Journal link 61 pages]

4.  J.-H. Choi, K.-H. Kim, J. Ryu, Sobolev regularity theory for the non-local elliptic and parabolic equations on C^{1,1} open sets. Discrete and Continuous Dynamical Systems, Volume 43, Issue 9, pages 3338-3377, 2023.  [arXiv link 42 pages, Journal link 40 pages]

5. J.-H. Choi, B.-S. Han, A regularity theory for stochastic partial differential equations with a super-linear diffusion coefficient and a spatially homogeneous colored noise. Stochastic Processes and their Applications, Volume 135, pages 1-30, 2021. [arXiv link 28 pages, Journal link 30 pages]

Preprints

1. J.-H. Choi, B.-S. Han, D. Park, Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noise and variable order non-local operators. [arXiv link 47 pages]

2. J.-H. Choi, I. Kim, An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity. [arXiv link 49 pages]

3. J.-H. Choi, A regularity theory for evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. [arXiv link 18 pages]

4. J.-H. Choi, J.B. Lee, J. Seo, K. Woo, On the trace theorem to Volterra type equations with local or non-local derivatives. [arXiv link 45 pages]

5. J.-H. Choi, J.B. Lee, J. Seo, K. Woo, Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. [arXiv link 36 pages]

6. J.-H. Choi, I.Kim, J.B. Lee, A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted Lp space. [arXiv link 47 pages]

Ongoing projects

1. J.-H. Choi, I. Kim, An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators driven by space-time white noise.

2. J.-H. Choi, J. Seo, Sobolev regularity theory for stochastic parabolic partial differential equations in non-smooth domains.

3. J.-H. Choi, J. Kang, D. Park, The domain of variable non-local operators related to subordinate Brownian motion on weighted Lebesgue spaces.

Collaborators (Alphabetical order)

• Beom-Seok Han (2), Assistant Professor at Sungshin Women's University

• Jaehoon Kang (1), BK Research Assistant Professor at Seoul National University

• Ildoo Kim (4), Associate Professor at Korea University

• Kyeong-Hun Kim (1), Professor at Korea University

• Jin Bong Lee (3), Postdoctoral Researcher at Seoul National University

• Daehan Park (2), Assistant Professor at Kangwon National University

• Junhee Ryu (1), Research Professor at Korea University

• Jinsol Seo (2), Research Fellow at Korea Institute for Advanced Study

• Kwan Woo (2), Postdoctoral Researcher at Ulsan National Institute of Science and Technology