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Représentation intégrale de fonctionnelles convexes sur un espace de mesures. II: Cas de l’épi-convergence. (Integral representation of convex functionals on a measure space. II: The case of epiconvergence). (French) Zbl 0721.49041
[For part I see the author, AVAMAC 86-11, Univ. de Perpignan (1986; Zbl 0721.49040).]
We state a general theorem of convergence for integral functionals on a space of measures. This is done thanks to a representation result for convex functionals F: \({\mathcal M}^ b\to [0,+\infty]\) which are lower semicontinuous with respect to the weak topology \(\sigma\) (\({\mathcal M}^ b,b_ 0)\) and satisfy the additivity condition \(F(\lambda_ 1+\lambda_ 2)=F(\lambda_ 1)+F(\lambda_ 2)\) whenever \(\lambda_ 1\perp \lambda_ 2\). Some duality arguments are developed in order to compute the limits and examples are detailed in relation with mechanics (reinforcement problems, fissured elastic bodies...).
Reviewer: G.Bouchitte

49Q20 Variational problems in a geometric measure-theoretic setting
46E27 Spaces of measures
74B20 Nonlinear elasticity
28A33 Spaces of measures, convergence of measures