A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients
In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂/∂xiaijx/ε,x∂uεx/∂xj=fx. Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoot...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8036814 |
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| _version_ | 1849398378218127360 |
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| author | Xiong Liu Wenming He |
| author_facet | Xiong Liu Wenming He |
| author_sort | Xiong Liu |
| collection | DOAJ |
| description | In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂/∂xiaijx/ε,x∂uεx/∂xj=fx. Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u0, we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u0 satisfies than the classical homogenization theory needs. |
| format | Article |
| id | doaj-art-a1ee6f15d1484c8a979bb4055901d3f5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a1ee6f15d1484c8a979bb4055901d3f52025-08-20T03:38:38ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/80368148036814A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic CoefficientsXiong Liu0Wenming He1School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, Guangdong 524048, ChinaSchool of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, Guangdong 524048, ChinaIn this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂/∂xiaijx/ε,x∂uεx/∂xj=fx. Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u0, we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u0 satisfies than the classical homogenization theory needs.http://dx.doi.org/10.1155/2021/8036814 |
| spellingShingle | Xiong Liu Wenming He A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients Journal of Function Spaces |
| title | A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients |
| title_full | A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients |
| title_fullStr | A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients |
| title_full_unstemmed | A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients |
| title_short | A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients |
| title_sort | new estimate for the homogenization method for second order elliptic problem with rapidly oscillating periodic coefficients |
| url | http://dx.doi.org/10.1155/2021/8036814 |
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