Abstract
For a large class of homogenization problems the given periodic matrix A(x) satisfies the usual inequality v1 I ≤ A(x) ≤ v2 I (v1, v2 > 0) at all points of ℝm outside certain subsets, called inclusions, where the matrix A(x) is degenerate. Two main types of degeneration are usually considered: if A(x) = 0, then we speak of soft inclusions, or a soft problem; if, on the other hand, the inverse matrix B = 0, then we are dealing with stiff inclusions, or a stiff problem. As a rule, the matrix A(x) is constant outside the inclusions, and therefore we have a kind of two-phase periodic medium.
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© 1994 Springer-Verlag Berlin Heidelberg
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Jikov, V.V., Kozlov, S.M., Oleinik, O.A. (1994). Elementary Soft and Stiff Problems. In: Homogenization of Differential Operators and Integral Functionals. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84659-5_3
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DOI: https://doi.org/10.1007/978-3-642-84659-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84661-8
Online ISBN: 978-3-642-84659-5
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