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Approximation of Young measures by functions and application to a problem of optimal design for plates with variable thickness

Published online by Cambridge University Press:  14 November 2011

E. Bonnetier  and
C. Conca
E. Bonnetier
Affiliation:
Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaideau cedex, France
C. Conca
Affiliation:
Universidad de Chile, Fac. de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170/3 Correo 3, Santiago, Chile
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Abstract

Given a parametrised measure and a family of continuous functions (φn), we construct a sequence of functions (uk) such that, as k→∞, the functions φn(uk) converge to the corresponding moments of the measure,in the weak * topology. Using the sequence (uk) corresponding to a dense family of continuous functions, a proof of the fundamental theorem for Young measures is given.

We apply these techniques to an optimal design problem for plates with variable thickness. The relaxation of the compliance functional involves three continuous functions of the thickness. We characterise a set of admissible generalised thicknesses, on which the relaxed functional attains its minimum.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 3 , 1994 , pp. 399 - 422
Copyright
Copyright © Royal Society of Edinburgh 1994

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