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Convergence Rates in L2 for Elliptic Homogenization Problems
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 DirichletExpand
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Boundary Estimates in Elliptic Homogenization
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 theExpand
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Periodic Homogenization of Green and Neumann Functions
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 NeumannExpand
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Homogenization of elliptic systems with Neumann boundary conditions
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, withExpand
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Estimates for the Stokes Operator in Lipschitz Domains
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 ∞ -estimatesExpand
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The Lp boundary value problems on Lipschitz domains
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 aExpand
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Resolvent Estimates in Lp for the Stokes Operator in Lipschitz Domains
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 resultExpand
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On the Neumann problem for Schr?odinger operators in Lipschitz domains
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 theExpand
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