Links between Young measures associated to constrained sequences

Anca-Maria Toader

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 579-590
  • ISSN: 1292-8119

Abstract

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We give necessary and sufficient conditions which characterize the Young measures associated to two oscillating sequences of functions, un on ω 1 × ω 2 and vn on ω 2 satisfying the constraint v n ( y ) = 1 | ω 1 | ω 1 u n ( x , y ) d x . Our study is motivated by nonlinear effects induced by homogenization. Techniques based on equimeasurability and rearrangements are employed.

How to cite

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Toader, Anca-Maria. "Links between Young measures associated to constrained sequences." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 579-590. <http://eudml.org/doc/197379>.

@article{Toader2010,
abstract = { 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. },
author = {Toader, Anca-Maria},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Young measures; rearrangements; doubly stochastic operators.; homogenization},
language = {eng},
month = {3},
pages = {579-590},
publisher = {EDP Sciences},
title = {Links between Young measures associated to constrained sequences},
url = {http://eudml.org/doc/197379},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Toader, Anca-Maria
TI - Links between Young measures associated to constrained sequences
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 579
EP - 590
AB - 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.
LA - eng
KW - Young measures; rearrangements; doubly stochastic operators.; homogenization
UR - http://eudml.org/doc/197379
ER -

References

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  7. J.V. Ryff, On the representation of doubly stochastic operators. Pacific J. Math.13 (1963) 1379-1386.  Zbl0125.08405
  8. J.V. Ryff, Orbits of L1-functions under doubly stochastic transformations. Trans. Amer. Math. Soc.117 (1965) 92-100.  Zbl0135.18804
  9. L. Tartar, Compensated compactness and applications to partial differential equations. Nonlinear Analysis and Mechanics: Heriot Watt Symposium, Vol. IV. Res. Notes in Math. Pitman (1979) 136-212.  
  10. L. Tartar, Memory effects and homogenization. Arch. Rational Mech. Anal.111 (1990) 121-133.  Zbl0725.45012
  11. M. Valadier, Young measures. Methods of Nonconvex Analysis, edited by A. Cellina. Springer Verlag, Lecture Notes in Math.1446 (1990) 152.  Zbl0738.28004

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