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 a epsilon-periodic lattice of highly conducting thin rods. The estimates are derived only at a distance epsilon^{1+tau} (for some tau>0) a...
| প্রধান লেখক: | , , |
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| বিন্যাস: | Journal article |
| প্রকাশিত: |
2011
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| _version_ | 1826266523456503808 |
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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 a epsilon-periodic lattice of highly conducting thin rods. The estimates are derived only at a distance epsilon^{1+tau} (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^p 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. 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^{1+tau} away from the fibres. |
| first_indexed | 2024-03-06T20:40:15Z |
| format | Journal article |
| id | oxford-uuid:340ce2c6-8b1b-41a1-a6e1-f757ec7c4d68 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:40:15Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:340ce2c6-8b1b-41a1-a6e1-f757ec7c4d682022-03-26T13:23:36ZInterior Regularity Estimates in High Conductivity Homogenization and ApplicationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:340ce2c6-8b1b-41a1-a6e1-f757ec7c4d68Symplectic Elements at Oxford2011Briane, MCapdeboscq, YNguyen, LIn this paper, uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by a epsilon-periodic lattice of highly conducting thin rods. The estimates are derived only at a distance epsilon^{1+tau} (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^p 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. 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^{1+tau} 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 |