Work

1. A regularity theory for space-time non-local evolution equations with anisotropic operator in mixed norm Sobolev spaces (with Jae-Hwan Choi, Jaehoon Kang, Daehan Park), 2025 (43 pages). [Link: arXiv(25-05)]

2. Green's function estimates for time measurable parabolic operators on polyhedrons and polyhedral cones (with Kyeong-Hun Kim, Kijung Lee), 2025 (41 pages). [Link: arXiv(25-03)]

3. Sobolev space theory for the heat and time-fractional heat equations in non-smooth domains, 2024 (62 pages). [Link: arXiv(24-11)]

4. Maximal operators given by Fourier multipliers with dilation of fractal dimensions (with Jin Bong Lee), 2024 (15 pages). [Link : arXiv(24-05)]

5. Sobolev space theory for Poisson's equation in non-smooth domains via superharmonic functions and Hardy's inequality, 2024 (58 pages). [Link: arXiv(24-03)]

6. Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness (with Jae-Hwan Choi, Jin Bong Lee, Kwan Woo), 2023 (36 pages). [Link: arXiv(23-09)]

7. On the trace theorem to Volterra-type equations with local or non-local derivatives (with Jae-Hwan Choi, Jin Bong Lee, Kwan Woo), 2023 (41 pages). [Link: arXiv(23-09)]

• Sobolev space theory for Poisson's and the heat equations in non-smooth domains via superharmonic functions and Hardy's inequality, 2023 (112 paes). [Link: arXiv(23-04)]

This paper will remain permanently unpublished; it is divided into Preprint 4 and Preprint 6.

1. Maximal operators associated with Fourier multipliers and applications (with Jin Bong Lee)

Journal of Functional Analysis, 2023 (37 pages). [Link : arXiv(22-06), Journal(23-01)] 

2. Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains (with Kyeong-Hun Kim, Kijung Lee) 

Journal of Differential Equations, 2022 (58 pages). [Link : arXiv(21-03), Journal(22-09)]

3. A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in R^d (with Kyeong-Hun Kim, Kijung Lee)

Journal of Differential Equations, 2021 (41 pages). [Link : arXiv(21-03), Journal(21-05)]

4. A refined Green's function estimate of the time measurable parabolic operators with conic domains (with Kyeong-Hun Kim, Kijung Lee)

Potential Analysis, 2022 (15 pages). [Link : arXiv(20-02), Journal(20-11)]

• Sobolev regularity theory for stochastic parabolic equations in non-smooth domains (with Jae-Hwan Choi)

• .... (with Jae-Hwan Choi, Chanwoo Kim, Dohyun Kwon)

• .... (with Chanwoo Kim)