Zhuolun Yang
Personal Info
I am a Prager Assistant Professor (postdoc position) at Division of Applied Math, Brown University. My mentor is Hongjie Dong. I received my Ph.D. at Rutgers University in 2021 under the supervision of Yanyan Li. You may find my CV here.
Contact Info
182 George Street, Room 323, Providence, RI 02912.
Email address: zhuolun_yang at brown dot edu
Research
My research interests lie in analysis, partial differential equations, and fluid dynamics. My current research focuses on the regularity of elliptic equations/systems, high-contrast composite materials, and the Navier-Stokes equation. I am open to learning and engaging in different directions within the field of PDEs.
Published or accepted papers:
Asymptotics of the solution to the perfect conductivity problem with p-Laplacian (With H.Dong and H.Zhu). To appear in Math. Ann. [arXiv]
Optimal gradient estimates of solutions to the insulated conductivity problem in dimensions greater than two (With H.Dong and Y.Y.Li). J. Eur. Math. Soc. (2024), published online first. [arXiv] [Journal]
The insulated conductivity problem with p-Laplacian (With H.Dong and H.Zhu). Arch. Ration. Mech. Anal. 247 (2023), 95 [arXiv] [Journal]
Optimal estimates for transmission problems including relative conductivities with different signs (With H.Dong). Adv. Math. 428 (2023), 109160. [arXiv] [Journal]
Gradient estimates of solutions to the insulated conductivity problem in dimensions greater than two (With Y.Y.Li). Math. Ann. 385 (2023), no. 3-4, 1775–1796. [arXiv] [Journal]
Regular solutions of the stationary Navier-Stokes equations on high dimensional Euclidean space (With Y.Y.Li). Commun. Math. Phys. 394 (2022), no. 2, 711–734. [arXiv] [Journal]
Gradient estimates of solutions to the conductivity problem with flatter insulators (With Y.Y.Li). Anal. Theory Appl. 37 (2021), no. 1, 114-128. [Journal]
Asymptotics of the gradient of solutions to the perfect conductivity problem (With H.G.Li and Y.Y.Li). Multiscale Model. Simul. 17 (2019), no. 3, 899-925. [arXiv] [Journal]
Preprints:
Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier-Stokes Equation in R^3 (With J.Bang). arXiv:2402.11144. [arXiv]
Gradient estimates for the insulated conductivity problem: The non-umbilical case (With H.Dong and Y.Y.Li). arXiv:2203.10081. [arXiv]