Jinping Zhuge

activity

20152026

most citedConvergence Rates in Periodic Homogenization of Systems of Elasticity

47 citations · 78 across the 28 of their papers we have counts for

collaborators

30 papers

math.AP2026

Quantitative homogenization of elliptic equations with infinitely many scales

Zhongwei Shen, Yao Xu, Jinping Zhuge

In this paper, we develop a general homogenization theory for elliptic equations with coefficients that oscillate periodically at infinitely many scales $\varepsilon = (\varepsilon…

math.AP2026

Large-scale harmonic measures and nontangential maximal functions in periodic homogenization

Zhongwei Shen, Jinping Zhuge

In this paper, we consider the elliptic operators $L_{ε} = - \nabla \cdot (A (X / ε) \nabla)$ with periodic coefficients in a bounded domain $Ω$ without any…

math.AP2026

Stability of $L^{p}$ Dirichlet problem under small bi-Lipschitz transformations of domains

Joseph Feneuil, Linhan Li, Jinping Zhuge

We show that small bi-Lipschitz deformations of a Lipschitz domain (with possibly large Lipschitz constant) preserve the solvability of the Dirichlet problem for the Laplacian with…

math.AP2025

Quantitative unique continuation for Neumann problem in planar $C^{1, α}$ domains

Yingying Cai, Jiuyi Zhu, Jinping Zhuge

In this paper, we study the quantitative unique continuation property of the second-order elliptic operators under the vanishing Neumann boundary condition over $C^{1, α}$ or convex…

math.AP2025

Optimal convergence rates in multiscale elliptic homogenization

Weisheng Niu, Yao Xu, Jinping Zhuge

This paper is devoted to the quantitative homogenization of multiscale elliptic operator $- \nabla \cdot A_{ε} \nabla$ , where $A_\varepsilon(x) = A(x/\varepsilon_1, x/\vareps…

math.AP2024

Wall laws for viscous flows in 3D randomly rough pipes: optimal convergence rates and stochastic integrability

Mitsuo Higaki, Yulong Lu, Jinping Zhuge

This paper is concerned with effective approximations and wall laws of viscous laminar flows in 3D pipes with randomly rough boundaries. The random roughness is characterized by th…

math.OC2024

Observability inequalities for heat equations with potentials

Jiuyi Zhu, Jinping Zhuge

This paper is mainly concerned with the observability inequalities for heat equations with time-dependent Lipschtiz potentials. The observability inequality for heat equations asse…

math.AP2024

Convergence rates of eigenvalue problems in perforated domains: the case of small volume

Zhongwei Shen, Jinping Zhuge

This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal…

math.AP2024

Uniform Calderón-Zygmund estimates in multiscale elliptic homogenization

Weisheng Niu, Jinping Zhuge

This paper is concerned with the elliptic equation $- div (A_{ε} \nabla u_{ε}) = div f$ in a bounded $C^{1}$ domain, where $A_{ε}$ takes a form o…

math.AP2024

The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes

Yingying Cai, Jinping Zhuge

Let $P$ be a bounded $n$ -dimensional Lipschitz polytope, and let $φ_{λ}$ be a Dirichlet Laplace eigenfunction in $P$ corresponding to the eigenvalue $λ$ . We show that the $(n - 1)$ -dim…

math.AP2023★ 1 cited

Uniform regularity for degenerate elliptic equations in perforated domains

Zhongwei Shen, Jinping Zhuge

This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectru…

math.AP2023

Nodal sets of Dirichlet eigenfunctions in quasiconvex Lipschitz domains

Jiuyi Zhu, Jinping Zhuge

We introduce the class of quasiconvex Lipschitz domains, which covers both $C^{1}$ and convex domains, to the study of boundary unique continuation for elliptic operators. In particu…

math.AP2023★ 1 cited

Spectral inequality for Schrödinger equations with power growth potentials

Jiuyi Zhu, Jinping Zhuge

We prove a spectral inequality for Schrödinger equations with power growth potentials, which particularly confirms a conjecture in \cite{DSV}. This spectral inequality depends on t…

math.AP2022★ 2 cited

Higher-order boundary layers and regularity for Stokes systems over rough boundaries

Mitsuo Higaki, Jinping Zhuge

In this paper, we study the large-scale boundary regularity for the Stokes system in periodically oscillating John domains. Our main contribution is the construction of boundary la…

math.AP2021

Compactness and stable regularity in multiscale homogenization

Weisheng Niu, Jinping Zhuge

In this paper we develop some new techniques to study the multiscale elliptic equations in the form of $- div (A_{ε} \nabla u_{ε}) = 0$ , where $A_\…

math.AP2021★ 1 cited

Large-scale regularity for the stationary Navier-Stokes equations over non-Lipschitz boundaries

Mitsuo Higaki, Christophe Prange, Jinping Zhuge

In this paper we address the large-scale regularity theory for the stationary Navier-Stokes equations in highly oscillating bumpy John domains. These domains are very rough, possib…

math.AP2021

Doubling inequalities and nodal sets in periodic elliptic homogenization

Carlos E. Kenig, Jiuyi Zhu, Jinping Zhuge

We prove explicit doubling inequalities and obtain uniform upper bounds (under $(d - 1)$ -dimensional Hausdorff measure) of nodal sets of weak solutions for a family of linear ellipti…

math.AP2020★ 1 cited

Regularity of a transmission problem and periodic homogenization

Jinping Zhuge

This paper is concerned with the regularity theory of a transmission problem arising in composite materials. We give a new self-contained proof for the $C^{k, α}$ estimates on both…

math.AP2020

Large-scale Regularity of Nearly Incompressible Elasticity in Stochastic Homogenization

Shu Gu, Jinping Zhuge

In this paper, we systematically study the regularity theory of the linear system of nearly incompressible elasticity. In the setting of stochastic homogenization, we develop new t…

math.AP2020

Regularity theory of elliptic systems in $ε$ -scale flat domains

Jinping Zhuge

We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the wea…

math.AP2019

Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains

Jinping Zhuge

In dimension two or three, the weak maximum principal for biharmonic equation is valid in any bounded Lipschitz domains. In higher dimensions (greater than three), it was only know…

math.AP2019★ 1 cited

Oscillatory integrals and periodic homogenization of Robin boundary value problems

Jun Geng, Jinping Zhuge

In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization the…

math.AP2018★ 1 cited

First-order expansions for eigenvalues and eigenfunctions in periodic homogenization

Jinping Zhuge

For a family of elliptic operators with periodically oscillating coefficients, $- div (A (\cdot / ε) \nabla)$ with tiny $ε > 0$ , we comprehensively study the…

math.AP2017★ 3 cited

Periodic homogenization of Green's functions for Stokes systems

Shu Gu, Jinping Zhuge

This paper is devoted to establishing the uniform estimates and asymptotic behaviors of the Green's functions $(G_{ε}, Π_{ε})$ (and fundamental solutions $(Γ_\vareps…

Quantitative homogenization of elliptic equations with infinitely many scales

Large-scale harmonic measures and nontangential maximal functions in periodic homogenization

Stability of Lp Dirichlet problem under small bi-Lipschitz transformations of domains

Quantitative unique continuation for Neumann problem in planar C1,α domains

Optimal convergence rates in multiscale elliptic homogenization

Wall laws for viscous flows in 3D randomly rough pipes: optimal convergence rates and stochastic integrability

Observability inequalities for heat equations with potentials

Convergence rates of eigenvalue problems in perforated domains: the case of small volume

Uniform Calderón-Zygmund estimates in multiscale elliptic homogenization

The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes

Uniform regularity for degenerate elliptic equations in perforated domains

Nodal sets of Dirichlet eigenfunctions in quasiconvex Lipschitz domains

Spectral inequality for Schrödinger equations with power growth potentials

Higher-order boundary layers and regularity for Stokes systems over rough boundaries

Compactness and stable regularity in multiscale homogenization

Large-scale regularity for the stationary Navier-Stokes equations over non-Lipschitz boundaries

Doubling inequalities and nodal sets in periodic elliptic homogenization

Regularity of a transmission problem and periodic homogenization

Large-scale Regularity of Nearly Incompressible Elasticity in Stochastic Homogenization

Regularity theory of elliptic systems in ε-scale flat domains

Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains

Oscillatory integrals and periodic homogenization of Robin boundary value problems

First-order expansions for eigenvalues and eigenfunctions in periodic homogenization

Periodic homogenization of Green's functions for Stokes systems

Stability of $L^{p}$ Dirichlet problem under small bi-Lipschitz transformations of domains

Quantitative unique continuation for Neumann problem in planar $C^{1, α}$ domains

Regularity theory of elliptic systems in $ε$ -scale flat domains