Junhee Ryu

About me

I am a Visiting Scholar at Brown University as well as a Research Professor at Korea University. 

I completed my Ph.D. in mathematics at Korea University in February 2023 under the supervision of Prof. Kyeong-hun Kim .

Employment

• Research Professor, Department of Mathematics, Korea University, 2024.03~ (Mentor: Kyeong-hun Kim)

• Post-Doctoral Fellow, Department of Mathematics, Korea University, 2023.03~2024.02 (Mentor: Kyeong-hun Kim)

Visiting Positions

• Visiting Scholar, Division of Applied Mathematics, Brown University, 2023.03~ (Hosted by Hongjie Dong)

Education

• Ph.D. in Mathematics, Korea University, 2017.03~2023.02 (Thesis Advisor: Kyeong-hun Kim)

• B.S. in Mathematics, Korea University, 2013.03~2016.08

Research Interests

• Deterministic and Stochastic Partial Differential Equations

• Space-time non-local equations on domains

• Non-local operators related to stochastic processes

• Degenerate equations

Preprints

1. (with K.-H. Kim) Weighted Sobolev space theory for non-local elliptic and parabolic equations with non-zero exterior condition on $C^{1,1}$ open sets [Arxiv]

Publications

1. (with H. Dong) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, accepted by SIAM J. Math. Anal. [Arxiv]

2. (with  K.-H. Kim and J.-H. Choi) Sobolev regularity theory for the non-local elliptic and parabolic equations on $C^{1,1}$ open sets, Discrete Contin. Dyn. Syst. 43(9), 2023 [Arxiv], [Journal]

3. (with K.-H. Kim and D. Park) A Sobolev space theory for the stochastic partial differential equations with space-time non-local operators, J. Evol. Equ. 22(57), 2022 [Arxiv], [Journal]

4. (with K.-H. Kim and D. Park) An $L_q (L_p)$-theory for diffusion equations with space-time nonlocal operators, J. Differ. Equ. 287, 2021 [Arxiv], [Journal]

Talks

1. (Invited) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, KIAS APP Seminar, January 18, 2024

2. (Contributed) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, JMM 2024, January 3-6, 2024

3. (Invited) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, KAIST PDE Seminar, December 12, 2023

4. (Invited) A Sobolev space theory for SPDEs with space-time non-local operators, Cornell Probability Seminar, December 4, 2023

5. (Contributed) Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces, The 19th Prairie Analysis Seminar, November 3-4, 2023

6. (Invited) Sobolev regularity theory for non-local equations on $C^{1,1}$ open sets, Conference on Probability and PDEs, April 20-21, 2023

7. (Invited) Sobolev regularity theory for non-local equations on $C^{1,1}$ open sets, Brown PDE Seminar, April 7, 2023

8. (Contributed) Sobolev space theory for the Dirichlet problem of the elliptic and parabolic equations with the fractional Laplacian on $C^{1,1}$ open sets, 2022 KMS Spring Meeting, April 28-29, 2022

9. (Contributed) Deterministic and stochastic parabolic equations with space-time non-local operators, 2021 KMS Annual Meeting, September 20-21, 2021

10. (Contributed) A Sobolev space theory for SPDEs with space-time nonlocal operators, Bernoulli-IMS 10th World Congress in Probability and Statistics, July 19-23, 2021

11. (Contributed) A Sobolev space theory for SPDEs with space-time nonlocal operators, 2021 KMS Spring Meeting, April 29-30, 2021

Referee for

• Calculus of Variations and Partial Differential Equations