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Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications

Published online by Cambridge University Press:  20 November 2018

R. Temam
R. Temam*
Affiliation:
Analyse Numérique Et Fonctionelle Cnrs Et Université Paris-SudBâtiment 425, 91405-Orsay, France
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Abstract

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In the first part of this article we recall the definition and a few basic properties of convex functionals defined on a space of bounded measures. In the second part we show several results of approximation of the following type: Although a measure μ cannot be approximated in the sense of the norm by smooth functions, we can find an appropriate sequence of smooth functions which converge weakly to the measure μ, the corresponding value of the functional converging to the value of the functional at μ.

This article is part of a series on the existence theory of solution of variational problems of mechanics (perfect plasticity), which is based on a systematic utilization of the methods of convex analysis and the calculus of variations.

Keywords

49A9928A99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 392 - 413
Copyright
Copyright © Canadian Mathematical Society 1982

References

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