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)...

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Những tác giả chính: Briane, M, Capdeboscq, Y, Nguyen, L
Định dạng: Journal article
Được phát hành: Springer Science+Business Media 2013
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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.
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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