Elementary Soft and Stiff Problems
For a large class of homogenization problems the given periodic matrix A(x) satisfies the usual inequality v1I ≤ A(x) ≤ v2I (v1, v2 > 0) at all points of ℝ m 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.
KeywordsVector Field Dirichlet Problem Integral Identity Homogenize Matrix Virtual Mass
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