Partial differential equations and homogenization theory
Jinping Zhuge's research lies at the intersection of partial differential equations, harmonic analysis, and homogenization theory. His work aims to understand the regularity, asymptotic behavior, and quantitative properties of solutions to certain partial differential equations in heterogeneous media and nonsmooth geometries. Particular interests include quantitative homogenization beyond classical periodic settings, boundary layer phenomena, multiscale analysis, spectral properties, and unique continuation.
Education:
2013/08-2019/06 Ph.D University of Kentucky
2010/09-2013/06 M.S. Nankai University
2006/09-2010/06 B.S Central South University
Employment
1. 2019/09-2022/06, L.E. Dickson Instructor, The University of Chicago
2. 2022/07-present, Associate Professor, Academy of Mathematics and Systems Science, Chinese Academy of Science.
Publications & Preprints:
1. Z. Shen, Y. Xu, J. Zhuge. Quantitative homogenization of elliptic equations with infinitely many scales. arXiv preprint arXiv:2605.02561, 2026
2. Z. Shen, J. Zhuge. Large-scale harmonic measures and nontangential maximal functions in periodic homogenization. arXiv preprint arXiv:2603.21902, 2026
3. J. Feneuil, L. Li, J. Zhuge. Stability of Dirichlet solvability under small bi-Lipschitz transformations of domains. arXiv preprint arXiv:2602.08115, 2026
4. Y. Cai, J. Zhu, J. Zhuge. Quantitative unique continuation for Neumann problem in planar C^{1,\alpha} domains. arXiv preprint arXiv:2512.07297, 2025
5. M. Higaki, Y. Lu, J. Zhuge. Wall laws for viscous flows in 3D randomly rough pipes: optimal convergence rates and stochastic integrability.Arch. Ration. Mech. Anal. Accepted, arXiv:2411.11653, 2024
6. J. Zhu, J. Zhuge. Nodal sets of Dirichlet eigenfunctions in quasiconvex Lipschitz domains. Adv. Math. 502, part B, 111150, 41pp, 2026
7. W. Niu, Y. Xu, J. Zhuge. Optimal convergence rates in multiscale elliptic homogenization. Comm. Pure Appl. Math. 79 (9), 2158-2222, 2026
8. Y. Cai, J. Zhuge. The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes. Math. Res. Lett. to appear, arXiv:2403.00279, 2024
9. W. Niu, J. Zhuge. Uniform Calder\'{o}n-Zygmund estimates in multiscale elliptic homogenization. Anal. PDE to appear, arXiv:2405.15149, 2024
10. J. Zhu, J. Zhuge. Spectral inequality for Schr\" odinger equations with power growth potentials. Indiana Univ. Math. J. 74 (5), 1467-1494, 2025
11. Z. Shen, J. Zhuge. Convergence rates of eigenvalue problems in perforated domains: the case of small volume. Adv. Nonlinear Stud. 25 (2), 364-408, 2025
12. Z. Shen, J. Zhuge. Uniform regularity for degenerate elliptic equations in perforated domains. Acta Math. Sin. (Engl. Ser.) 41 (1), 378-412, 2025
13. J. Zhu, J. Zhuge. Observability inequalities for heat equations with potentials. ESAIM Control Optim. Calc. Var. to appear, arXiv:2409.09476, 2024
14. M. Higaki, C. Prange, J. Zhuge. Large-scale regularity for the stationary Navier–Stokes equations over non-Lipschitz boundaries. Anal. PDE 17 (1), 171-242, 2024
15. M. Higaki, J. Zhuge. Higher-order boundary layers and regularity for Stokes systems over rough boundaries. Arch. Ration. Mech. Anal. 247 (4), Paper No. 66, 61 pp. 2023
16. W. Niu, J. Zhuge. Compactness and stable regularity in multiscale homogenization. Math. Ann. 385 (3), 1-43, 2023
17. S. Gu, J. Zhuge. Large-scale regularity of nearly incompressible elasticity in stochastic homogenization. Arch. Ration. Mech. Anal. 244 (3), 1311-1372, 2022
18. C. E. Kenig, J. Zhu, J. Zhuge. Doubling inequalities and nodal sets in periodic elliptic homogenization. Comm. Partial Differential Equations 47 (3), 549-584, 2022
19. J. Zhuge. Regularity of a transmission problem and periodic homogenization. J. Math. Pures Appl. (9) 153, 213-247, 2021
20. J. Zhuge. Regularity theory of elliptic systems in ε-scale flat domains. Adv. Math. 379, 107566, 2021
21. J. Zhuge. Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains. J.Funct. Anal. 279 (12), 108786, 2020
22. J. Zhuge. First-order expansions for eigenvalues and eigenfunctions in periodic homogenization. Proc. Roy. Soc. Edinburgh Sect. A 150 (5), 2189-2215, 2020
23. Z. Shen, J. Zhuge. Regularity of homogenized boundary data in periodic homogenization of elliptic systems. J. Eur. Math. Soc. (JEMS) 22 (9), 2751-2776, 2020
24. J. Geng, J. Zhuge. Oscillatory integrals and periodic homogenization of Robin boundary value problems. SIAM J. Math. Anal. 52 (1), 104-134, 2020
25. S. Gu, J. Zhuge. Periodic homogenization of Green's functions for Stokes systems. Calc. Var. Partial Differential Equations 58 (3), Paper No. 114, 46 pp, 2019
26. Z. Shen, J. Zhuge. Boundary layers in periodic homogenization of Neumann problems. Comm. Pure Appl. Math. 71 (11), 2163-2219, 2018
27. J. Zhuge. Homogenization and boundary layers in domains of finite type. Comm. Partial Differential Equations 43 (4), 549-584, 2018
28. Z. Shen, J. Zhuge. Approximate correctors and convergence rates in almost-periodic homogenization. J. Math. Pures Appl. 110, 187-238, 2018
29. Z. Shen, J. Zhuge. Convergence rates in periodic homogenization of systems of elasticity. Proc. Amer. Math. Soc. 145 (3), 1187-1202, 2017
30. J. Zhuge. Uniform boundary regularity in almost-periodic homogenization. J. Differential Equations 262 (1), 418-453, 2017
31. J. Zhuge, Z. Zhang. Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms. Internat. J. Math. 27 (02), 1650010, 2016
