Open AccessTwo scale defect measure and linear equations with oscillating coefficients
Author(s) -
Jelena Aleksić,
Stevan Pilipović
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909867a
Subject(s) - mathematics , torus , measure (data warehouse) , scalar (mathematics) , mathematical analysis , limit (mathematics) , scale (ratio) , operator (biology) , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , database , computer science , transcription factor , gene
Microlocal measure ? is associated to a two-scale convergent sequence un over Rd with the limit u ? L2(Rd x Td), Td is a torus, to analyze possible strong limit. ? is an operator valued measure absolutely continuous with respect to the product of scalar microlocal defect measure and a measure on the d-dimensional torus. The result is applied to the first order linear PDE with the oscillating coefficients.