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Convergence of monotone operators with respect to measures
Author(s) -
Mamchaoui Mohamed,
Senouci Bereksi Ghouti
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600112
Subject(s) - monotone polygon , homogenization (climate) , mathematics , convergence (economics) , operator theory , operator norm , commutative property , pure mathematics , mathematical analysis , geometry , biodiversity , ecology , economics , biology , economic growth
This paper deals with monotone operators in the theory of homogenization. The operators introduced may depend on a small parameter δ. We establish some convergence results with respect to singular measures. Our result is valid without using the two‐scale convergence. A comparison between the operators for the singular structure and the classical ones is obtained when the thickness δ of the structure vanishes. Finally, under some suitable assumptions, we show the commutativity of the corresponding diagram.