8 citations · 31 across the 16 of their papers we have counts for
17 papers
Fundamental solution expansions in stochastic homogenization of parabolic systems with time-dependent coefficients
Junxin Pan, Li Wang, Qiang Xu
This paper studies fundamental solutions of uniformly parabolic systems with stationary random coefficients depending on space and time. Under ergodicity and local regularity, we e…
Calderon-Zygmund estimates for stochastic elliptic systems on bounded Lipschitz domains
Li Wang, Qiang Xu
Concerned with elliptic operators with stationary random coefficients of integrable correlations and bounded Lipschitz domains, arising from stochastic homogenization theory, this…
Bias in the representative volume element method: periodize the ensemble instead of its realizations
Nicolas Clozeau, Marc Josien, Felix Otto +1
We study the Representative Volume Element (RVE) method, which is a method to approximately infer the effective behavior of a stationary random medium. The latter…
Corrector estimates and homogenization errors of unsteady flow ruled by Darcy's law
Li Wang, Qiang Xu, Zhifei Zhang
Focusing on Darcy's law incorporating memory effects, this paper studies non-stationary Stokes equations on perforated domains. We establish a sharp homogenization error for both v…
suboptimal error estimates for homogenization of linear elasticity systems on perforated domains
Li Wang, Qiang Xu, Peihao Zhao
In the present work, we established almost-sharp error estimates for linear elasticity systems in periodically perforated domains. The first result was -error…
Quantitative estimates for homogenization of nonlinear elliptic operators in perforated domains
Li Wang, Qiang Xu, Peihao Zhao
This paper was devoted to study the quantitative homogenization problems for nonlinear elliptic operators in perforated domains. We obtained a sharp error estimate …
Convergence rates on periodic homogenization of p-Laplace type equations
Li Wang, Qiang Xu, Peihao Zhao
In this paper, we find some error estimates for periodic homogenization of p-Laplace type equations under the same structure assumption on homogenized equations. The main idea is t…
Quantitative Estimates on Periodic Homogenization of Nonlinear Elliptic Operators
Li Wang, Qiang Xu, Peihao Zhao
In this paper, we are interested in the periodic homogenization of quasilinear elliptic equations. We obtain error estimates for a domain, and $O(\…
Neumann Problems in Homogenization of General Elliptic Systems
Qiang Xu, Shulin Zhou
In this paper, we extend the nontangential maximal function estimate obtained by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic operators with rapidly o…
The Methods of Layer Potentials for General Elliptic Homogenization Problems in Lipschitz Domains
Qiang Xu, Peihao Zhao, Shulin Zhou
In terms of layer potential methods, this paper is devoted to study the boundary value problems for nonhomogeneous elliptic operators with rapidly oscillating coefficients in…
Quantitative Estimates in Homogenization of Parabolic Systems of Elasticity in Lipschitz Cylinders
Qiang Xu, Shulin Zhou
In a Lipschitz cylinder, this paper is devoted to establish an almost sharp error estimate in -norm for parabolic systems of elasticity w…
Commutator Estimates for the Dirichlet-to-Neumann Map of Stokes Systems in Lipschitz Domains
Qiang Xu, Weiren Zhao, Shulin Zhou
In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's bilinear estimates, and…
Optimal Boundary Estimates for Stokes Systems in Homogenization Theory
Shu Gu, Qiang Xu
The paper concerns the sharp boundary regularity estimates in homogenization of Dirichlet problem for Stokes systems. We obtain the Lipschitz estimates for velocity term and $L^\in…
Convergence rates and estimates in homogenization theory of Stokes systems in Lipschitz domains
Qiang Xu
Concerned with the Stokes systems with rapidly oscillating periodic coefficients, we mainly extend the recent works in \cite{SGZWS,G} to those in term of Lipschitz domains. The arg…
Convergence rates for general elliptic homogenization problems in a bounded Lipschitz domain
Qiang Xu
The paper extends the results obtained by C. Kenig, F. Lin and Z. Shen in \cite{SZW2} to more general elliptic homogenization problems in two perspectives: lower order terms in the…
Uniform Regularity Estimates in Homogenization Theory of Elliptic System with Lower Order terms
Qiang Xu
In this paper, we extend the uniform regularity estimates obtained by M. Avellanda and F. Lin in the paper of Compactness methods in the theory of homogenization (Comm. Pure Appl.…
Uniform Regularity Estimates in Homogenization Theory of Elliptic Systems with Lower Order Terms on the Neumann Boundary Problem
Qiang Xu
In this paper, we mainly employed the idea of the previous paper to study the sharp uniform estimates with for more general elliptic systems with the Neu…