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Interior Regularity Estimates in High Conductivity Homogenization and Application

Abstract:

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 di...

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Publication status:
Published

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Publisher copy:
10.1007/s00205-012-0553-0

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Journal:
Archive for Rational Mechanics and Analysis
Volume:
207
Issue:
1
Pages:
75-137
Publication date:
2011-10-06
DOI:
EISSN:
1432-0673
ISSN:
0003-9527
URN:
uuid:340ce2c6-8b1b-41a1-a6e1-f757ec7c4d68
Source identifiers:
184998
Local pid:
pubs:184998

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