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generalized boundary layers

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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The boundary behavior of a composite material
Maria Neuss-Radu
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 3 / May 2001

Published online by Cambridge University Press:

15 April 2002, pp. 407-435

Print publication:

May 2001
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In this paper, we study how solutions to elliptic problems withperiodically oscillating coefficients behave inthe neighborhood of the boundary of a domain. We extend theresults known for flat boundaries to domains with curved boundariesin the case of a layered medium. This is done by generalizing thenotion of boundary layer and by defining boundary correctors whichlead to an approximation of order ε in the energy norm.