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Links between Young measures associated to constrained sequences

Published online by Cambridge University Press:  15 August 2002

Anca-Maria Toader
Anca-Maria Toader*
Affiliation:
Faculdade de Ciências, CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal; [email protected].
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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.

Keywords

Young measuresrearrangementsdoubly stochastic operators.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 579 - 590
Copyright
© EDP Sciences, SMAI, 2000

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References

Amirat, Y., Hamdache, K. and Ziani, A., Some Results on Homogenization of Convection-Diffusion Equations. Arch. Rational Mech. Anal. 114 (1991) 155-178. CrossRef
E.J. Balder, Lectures on Young measures. Preprint No. 9517, CEREMADE. Université Paris IX - Dauphine, France (1995).
J.M. Ball, A version of the fundamental theorem for Young measures, Partial Differential Equations and Continuum Models of Phase Transitions, edited by M. Rascle, M. Slemrod and D. Serre. Springer Verlag, Berlin (1989) 207-215.
Cartier, P., Fell, J.M.G. and Meyer, P.A., Comparaison des mesures portées par un ensemble convexe compact. Bull. Soc. Math. France 92 (1964) 435-445. CrossRef
G.H. Hardy, J.E. Littlewood and G.E. Pólya, Inequalities. Cambridge (1952).
P.A. Meyer, Probabilités et potentiel. Hermann, Paris (1966).
Ryff, J.V., On the representation of doubly stochastic operators. Pacific J. Math. 13 (1963) 1379-1386. CrossRef
Ryff, J.V., Orbits of L 1-functions under doubly stochastic transformations. Trans. Amer. Math. Soc. 117 (1965) 92-100.
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.
Tartar, L., Memory effects and homogenization. Arch. Rational Mech. Anal. 111 (1990) 121-133. CrossRef
Valadier, M., Young measures. Methods of Nonconvex Analysis, edited by A. Cellina. Springer Verlag, Lecture Notes in Math. 1446 (1990) 152. CrossRef