Abstract
This article treats (without proofs) two problems, where the results of homogenization are formulated as the result of “strong two-scale resolvent convergence” of the corresponding operators. Attention is mainly paid to the convergence of spectra under homogenization.
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REFERENCES
Kato E., Theory of Perturbations of Linear Operators[Russian translation ], Mir, Moscow (1972).
Zhikov V.V.,“On an extension and applications of the method of two-scale convergence,” Mat.Sb., 191, No.7, 31–72 (2000).
Bakhvalov N.S. and Panasenko G.P., Averaging of Processes in Periodic Media[in Russian], Nauka, Moscow (1984).
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Zhikov, V.V. Two-Scale Convergence and Spectral Questions of the Homogenization Theory. Journal of Mathematical Sciences 114, 1450–1460 (2003). https://doi.org/10.1023/A:1022252912311
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DOI: https://doi.org/10.1023/A:1022252912311