Interior Regularity Estimates in High Conductivity Homogenization and Application
In this paper, uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by an (Epsilon)-periodic lattice of highly conducting thin rods. The estimates are derived only at a distance (Epsilon) (for some (Tau) > 0)...
| Hoofdauteurs: | , , |
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| Formaat: | Journal article |
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Springer Science+Business Media
2013
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| _version_ | 1826301261329203200 |
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| author | Briane, M Capdeboscq, Y Nguyen, L |
| author_facet | Briane, M Capdeboscq, Y Nguyen, L |
| author_sort | Briane, M |
| collection | OXFORD |
| description | In this paper, uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by an (Epsilon)-periodic lattice of highly conducting thin rods. The estimates are derived only at a distance (Epsilon) (for some (Tau) > 0) away from the fibres. This distance constraint is rather sharp since the gradients of the solutions are shown to be unbounded locally in L as soon as p > 2. One key ingredient is the derivation in dimension two of regularity estimates to the solutions of the equations deduced from a Fourier series expansion with respect to the fibres' direction, and weighted by the high-contrast conductivity. The dependence on powers of (Epsilon) of these two-dimensional estimates is shown to be sharp. The initial motivation for this work comes from imaging, and enhanced resolution phenomena observed experimentally in the presence of micro-structures (Lerosey et al., Science 315:1120-1124, 2007). We use these regularity estimates to characterize the signature of low volume fraction heterogeneities in the fibred reinforced medium, assuming that the heterogeneities stay at a distance (Epsilon) away from the fibres. |
| first_indexed | 2024-03-07T05:29:43Z |
| format | Journal article |
| id | oxford-uuid:e1d2f36c-eeee-4d9f-854a-9d43f51b7301 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:29:43Z |
| publishDate | 2013 |
| publisher | Springer Science+Business Media |
| record_format | dspace |
| spelling | oxford-uuid:e1d2f36c-eeee-4d9f-854a-9d43f51b73012022-03-27T09:56:54ZInterior Regularity Estimates in High Conductivity Homogenization and ApplicationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e1d2f36c-eeee-4d9f-854a-9d43f51b7301Symplectic Elements at OxfordSpringer Science+Business Media2013Briane, MCapdeboscq, YNguyen, LIn this paper, uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by an (Epsilon)-periodic lattice of highly conducting thin rods. The estimates are derived only at a distance (Epsilon) (for some (Tau) > 0) away from the fibres. This distance constraint is rather sharp since the gradients of the solutions are shown to be unbounded locally in L as soon as p > 2. One key ingredient is the derivation in dimension two of regularity estimates to the solutions of the equations deduced from a Fourier series expansion with respect to the fibres' direction, and weighted by the high-contrast conductivity. The dependence on powers of (Epsilon) of these two-dimensional estimates is shown to be sharp. The initial motivation for this work comes from imaging, and enhanced resolution phenomena observed experimentally in the presence of micro-structures (Lerosey et al., Science 315:1120-1124, 2007). We use these regularity estimates to characterize the signature of low volume fraction heterogeneities in the fibred reinforced medium, assuming that the heterogeneities stay at a distance (Epsilon) away from the fibres. |
| spellingShingle | Briane, M Capdeboscq, Y Nguyen, L Interior Regularity Estimates in High Conductivity Homogenization and Application |
| title | Interior Regularity Estimates in High Conductivity Homogenization and Application |
| title_full | Interior Regularity Estimates in High Conductivity Homogenization and Application |
| title_fullStr | Interior Regularity Estimates in High Conductivity Homogenization and Application |
| title_full_unstemmed | Interior Regularity Estimates in High Conductivity Homogenization and Application |
| title_short | Interior Regularity Estimates in High Conductivity Homogenization and Application |
| title_sort | interior regularity estimates in high conductivity homogenization and application |
| work_keys_str_mv | AT brianem interiorregularityestimatesinhighconductivityhomogenizationandapplication AT capdeboscqy interiorregularityestimatesinhighconductivityhomogenizationandapplication AT nguyenl interiorregularityestimatesinhighconductivityhomogenizationandapplication |