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doubly stochastic operators.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Links between Young measures associated to constrained sequences
Anca-Maria Toader
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 5 / 2000

Published online by Cambridge University Press:

15 August 2002, pp. 579-590

Print publication:

2000
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We give necessary and sufficient conditions which characterize the Young measures associated to two oscillating sequences of functions, un on $\omega_1\times \omega_2$ and vn on $\omega_2$ satisfying the constraint $v_n(y)=\frac{1}{|\omega_1|} \int_{\omega_1} u_n (x, y) dx$. Our study is motivated by nonlinear effects induced by homogenization. Techniques based on equimeasurability and rearrangements are employed.