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A new estimate for the homogenization method for second-order elliptic problem with rapidly oscillating periodic coefficients. (English) Zbl 1473.35147

Summary: In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form \(( \partial / \partial x_i)(a^{ij} (x /\varepsilon, x)(\partial u^\varepsilon (x)/\partial x_j))=f(x)\). Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution \(u^0\), we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution \(u^0\) satisfies than the classical homogenization theory needs.

MSC:

35J15 Second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
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