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- Publications
- Influence

Convergence Rates in L2 for Elliptic Homogenization Problems

- C. Kenig, F. Lin, Zhongwei Shen
- Mathematics
- 28 February 2011

We study rates of convergence of solutions in L2 and H1/2 for a family of elliptic systems $${\{\mathcal{L}_\varepsilon\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet… Expand

Boundary Estimates in Elliptic Homogenization

- Zhongwei Shen
- Mathematics
- 4 May 2015

For a family of systems of linear elasticity with rapidly oscillating periodic coefficients, we establish sharp boundary estimates with either Dirichlet or Neumann conditions, uniform down to the… Expand

Periodic Homogenization of Green and Neumann Functions

- C. Kenig, F. Lin, Zhongwei Shen
- Mathematics
- 1 August 2014

For a family of second-order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann functions, using Dirichlet and Neumann… Expand

Homogenization of elliptic systems with Neumann boundary conditions

- C. Kenig, F. Lin, Zhongwei Shen
- Mathematics
- 29 October 2010

The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators $\{\mathcal{L}_\varepsilon, \varepsilon>0\}$, arising in the theory of homogenization, with… Expand

Estimates for the Stokes Operator in Lipschitz Domains

- R. Brown, Zhongwei Shen
- Mathematics
- 1995

We study the Stokes operator A in a three- dimensional Lipschitz domain Ω. Our main result asserts that the domain of A is contained in W 1,p 0 (Ω) ∩ W 3/2,2 (Ω) for some p> 3. Certain L ∞ -estimates… Expand

Boundary value problems for parabolic Lamé systems and a nonstationary linearized system of Navier-Stokes equations in Lipschitz cylinders

- Zhongwei Shen
- Mathematics
- 1 April 1991

The Lp boundary value problems on Lipschitz domains

- Zhongwei Shen
- Mathematics
- 26 April 2006

Abstract Let Ω be a bounded Lipschitz domain in R n . We develop a new approach to the invertibility on L p ( ∂ Ω ) of the layer potentials associated with elliptic equations and systems in Ω. As a… Expand

Resolvent Estimates in Lp for the Stokes Operator in Lipschitz Domains

- Zhongwei Shen
- Mathematics
- 16 February 2012

We establish the Lp resolvent estimates for the Stokes operator in Lipschitz domains in $${\mathbb{R}^d}$$, $${d\geqq 3}$$ for $${|\frac{1}{p}-\frac{1}{2}| < \frac{1}{2d} +\varepsilon}$$. The result… Expand

On the Neumann problem for Schr?odinger operators in Lipschitz domains

- Zhongwei Shen
- Physics
- 1994

1,176,952. Waveguide dissipative loads. MARCONI CO. Ltd. 17 June, 1968 [10 July, 1967], No. 31686/67. Heading H1W. A liquid power-absorbing load comprises a low-loss dielectric body for guiding the… Expand

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