Research Interest
I am currently interested in the regularity theory of partial differential equations, including but not limited to the following:
Degenerate elliptic and parabolic equations
Elliptic problems in high contrast composite materials
Fluid dynamics, small scale creations
Mixing, enhanced dissipation, and inviscid damping
1. Gradient estimates for the insulated conductivity problem with partially flat inclusions, with Hongjie Dong and Zhuolun Yang, submitted (2025). ArXiv:2508.12700.
2. Gradient estimates for the conductivity problem with imperfect bonding interfaces, with Hongjie Dong and Zhuolun Yang, submitted (2024). ArXiv:2409.05652.
3. Asymptotics of the solution to the perfect conductivity problem with p-Laplacian, with Hongjie Dong and Zhuolun Yang, Math. Ann. 390 (2024), no. 4, 5005–5051.
4. The insulated conductivity problem with p-Laplacian, with Hongjie Dong and Zhuolun Yang, Arch. Ration. Mech. Anal. 247 (2023), no. 5, Paper No. 95, 46 pp.
5. Gradient estimates for singular parabolic p-Laplace type equations with measure data, with Hongjie Dong, Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 86, 41 pp.
6. Gradient estimates for singular p-Laplace type equations with measure data, with Hongjie Dong, J. Eur. Math. Soc. (JEMS), 26 (2024), no. 10, 3939–3985.
Talks and Presentations
Overseas Alumni Academic Forum, School of Mathematics, Nanjing University, Nanjing, China, June 2025
International Workshop on Advances in Fluid Mechanics, Duke Kunshan University, Kunshan, China, May 2025
Applied and Computational Mathematics Seminar, University of South Carolina, April 2025
Applied Math & Analysis Seminar, Duke University, December 2024
International Conference on PDEs related to Material Sciences, Beijing Normal University, Beijing, China, June 2024
AMS Special Session on Dynamics and Regularity of PDEs, Joint Mathematics Meetings, San Francisco, CA, January 2024
PDE/Differential geometry seminar, University of Connecticut, October 2023
PDE seminar, Brown University, September 2023
Early Career Math Colloquium, University of Arizona, October 2022
AMS Fall Southeastern Sectional Meeting, Chattanooga, TN, October 2022
Recent Trends in Partial Differential Equations Summer School, Duke University, August 2022
PIMS-IFDS-NSF Summer School on Optimal Transport, University of Washington at Seattle, June 2022
PDE seminar, Brown University, February 2021