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On uniform H2-estimates in periodic homogenization

Published online by Cambridge University Press:  12 July 2007

C. Conca  and
M. Vanninathan
C. Conca
Affiliation:
Departamento de Ingeniería Matemática, and CMM, UMR 2071 CNRS-UChile, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
M. Vanninathan
Affiliation:
IISc-TIFR Mathematics Programme, TIFR Centre, PO Box 1234, Bangalore 560012, India
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Abstract

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We introduce what are called regular materials for which, by definition, the corresponding solution of the classical periodic homogenization problem remains bounded in . We give examples of two types of such materials depending on whether the coefficients representing them belong to W1,∞ or not. A complete characterization is obtained in the former case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 3 , June 2001 , pp. 499 - 517
Copyright
Copyright © Royal Society of Edinburgh 2001