Skip to main content Accessibility help
×
Home

Links between Young measures associated to constrained sequences

  • Anca-Maria Toader (a1)

Abstract

We give necessary and sufficient conditions which characterize the Young measures associated to two oscillating sequences of functions, u n on $\omega_1\times \omega_2$ and v n 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.

Copyright

References

Hide All
[1] Amirat, Y., Hamdache, K. and Ziani, A., Some Results on Homogenization of Convection-Diffusion Equations. Arch. Rational Mech. Anal. 114 (1991) 155-178.
[2] E.J. Balder, Lectures on Young measures. Preprint No. 9517, CEREMADE. Université Paris IX - Dauphine, France (1995).
[3] 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.
[4] 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.
[5] G.H. Hardy, J.E. Littlewood and G.E. Pólya, Inequalities. Cambridge (1952).
[6] P.A. Meyer, Probabilités et potentiel. Hermann, Paris (1966).
[7] Ryff, J.V., On the representation of doubly stochastic operators. Pacific J. Math. 13 (1963) 1379-1386.
[8] Ryff, J.V., Orbits of L 1-functions under doubly stochastic transformations. Trans. Amer. Math. Soc. 117 (1965) 92-100.
[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] Tartar, L., Memory effects and homogenization. Arch. Rational Mech. Anal. 111 (1990) 121-133.
[11] Valadier, M., Young measures. Methods of Nonconvex Analysis, edited by A. Cellina. Springer Verlag, Lecture Notes in Math. 1446 (1990) 152.

Keywords

Links between Young measures associated to constrained sequences

  • Anca-Maria Toader (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.