Homogenization of elliptic systems with Neumann boundary conditions

By Carlos E. Kenig, F. Lin, Zhongwei Shen. 2010

156 citations recorded by the source corpus.

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 rapidly oscillating periodic coefficients. We establish sharp $W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates, which are uniform in the parameter $\varepsilon$, on solutions with Neumann boundary conditions in $C^{1,\alpha}$ domains.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/239bc13b08bcb0413e4943a3d8a5e120640f08b0

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In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Lipschitz Regularity for Elliptic Equations with Random Coefficients (2014, methodology): “[28] C. Kenig, F. Lin, and Z. Shen.”
Stokes Resolvent Estimates in Spaces of Bounded Functions (2012, background): “eorems (Theorem 1.1–Theorem 1.3) are also valid for a perturbed half space with C3-boundary forn ≥ 3. (ii) After this work was completed, the authors were informed of the recent paper by Kenig et al. [25], where the estimate (1.6) was proved for C1,γ-bounded domains by estimating the Green function ”
Periodic Homogenization of Green and Neumann Functions (2014, background): “The results rely on the uniform L and Neumann function estimates obtained in [19,22] under the additional symmetry condition A D A.”
Lipschitz Estimates in Almost‐Periodic Homogenization (2014, methodology): “We refer the reader to [16] for the proof in the periodic setting.”