# Jinping Zhuge

My name is Jinping Zhuge. I am currently an associate professor at Morningside Center of Mathematics, the Academy of Mathematics and Systems Science of Chinese Academy of Sciences. Please see my CV here. I received my Ph.D degree in the University of Kentucky in 2019 under the supervision of Zhongwei Shen. From 2019 to 2022, I was an L. E. Dickson Instructor at the University of Chicago mentored by Carlos Kenig and Charles Smart.

Email: jpzhuge@amss.ac.cn

Research:

My research interests lie in partial differential equations and harmonic analysis, particularly in homogenization theory. The following are my publications and preprints.

Preprints:

Convergence rates of eigenvalue problems in perforated domains: the case of small volume (with Zhongwei Shen), arXiv:2408.14278, 2024.

Uniform Calderón-Zygmund estimates in multiscale elliptic homogenization (with Weisheng Niu), arXiv:2405.15149, 2024.

The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes (with Yingying Cai), arXiv:2403.00279, 2024.

Uniform regularity for degenerate elliptic equations in perforated domains (With Zhongwei Shen), Acta Math. Sin. (Engl. Ser.), to appear. arXiv:2311.10258, 2023.

Nodal sets of Dirichlet eigenfunctions in quasiconvex Lipschitz domains (with Jiuyi Zhu), arXiv:2303.02046, 2023.

Spectral inequality for Schrödinger equations with power growth potentials (with Jiuyi Zhu), Indiana Univ. Math. J., accepted. arXiv:2301.12338, 2023.

Publications:

Large-scale regularity for the stationary Navier-Stokes equations over non-Lipschitz boundaries (with Mitsuo Higaki and Christophe Prange). Anal. PDE, 2024.

Higher-order boundary layers and regularity for Stokes systems over rough boundaries (with Mitsuo Higaki). Arch. Ration. Mech. Anal., 2023.

Compactness and stable regularity in multiscale homogenization (with Weisheng Niu), Math. Ann., 2023.

Large-scale regularity of nearly incompressible elasticity in stochastic homogenization (with Shu Gu). Arch. Ration. Mech. Anal., 2022.

Doubling inequalities and nodal sets in periodic elliptic homogenization (with Carlos Kenig and Jiuyi Zhu). Comm. Partial Differential Equations, 2022.

Regularity of a transmission problem and periodic homogenization. J. Math. Pures Appl., 2021.

Regularity theory of elliptic systems in ε-scale flat domains. Adv. Math., 2021.

Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains. J. Functional Analysis, 2020.

Regularity of homogenized boundary data in periodic homogenization of elliptic systems (with Zhongwei Shen). J. Eur. Math. Soc., 2020.

Oscillatory integrals and periodic homogenization of Robin boundary value problems (with Jun Geng). SIAM J. Math. Anal., 2020.

First-order expansions for eigenvalues and eigenfunctions in periodic homogenization. Proc. Roy. Soc. Edinburgh Sect. A, 2020.

Periodic homogenization of Green's functions for Stokes systems (with Shu Gu). Calc. Var. Partial Differential Equations, 2019.

Homogenization and boundary layers in domains of finite type. Comm. Partial Differential Equations, 2018.

Boundary layers in periodic homogenization of Neumann problems (with Zhongwei Shen). Comm. Pure Appl. Math., 2018.

Approximate correctors and convergence rates in almost-periodic homogenization (with Zhongwei Shen). J. Math. Pures Appl., 2018.

Uniform boundary regularity in almost-periodic homogenization. J. Differential Equations, 2017.

Convergence rates in periodic homogenization of systems of elasticity (with Zhongwei Shen). Proc. Amer. Math. Soc., 2017.

Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms (with Zhenqiu Zhang). Internat. J. Math., 2016.

Doctoral Dissertation: