4 papers
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…
Large-scale harmonic measures and nontangential maximal functions in periodic homogenization
Zhongwei Shen, Jinping Zhuge
In this paper, we consider the elliptic operators with periodic coefficients in a bounded domain without an…
The Magnetic Laplacian with a Higher-order Vanishing Magnetic Field in a Bounded Domain
Zhongwei Shen
This paper is concerned with spectrum properties of the magnetic Laplacian with a higher-order vanishing magnetic field in a bounded domain. We study the asymptotic behaviors of gr…
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…