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Zolesio, Introduction to shape optimization. Shape sensitivity analysis, Springer Series in Computational Mathematics 16, Springer Verlag, New York (1992). [24] L. Tartar, Estimations Fines des Coe´ fficients Homoge´ ne´ ise´ s, Ennio de Giorgi colloquium, P. , Pitman Research Notes in Math. 168-187 (1985). C. B. Saunders, Philadelphia (1969). Andrea BRAIDES Dipartimento di Elettronica per l’Automazione Universit`a di Brescia Via Valotti, 9 25060 BRESCIA (ITALY) An Introduction to Homogenization and Gamma-convergence School on Homogenization ICTP, Trieste, September 6–17, 1993 CONTENTS 1.

4) If F = Γ(d)- limh Fh and G is any d-continuous function then Γ(d)- limh (Fh + G) = F + G (this remark will be extremely useful in applications). 5) The Γ-limit of a sequence of convex functions is convex (here and in the following, we suppose that (X, d) is a topological vector space). , Fh (x +y) +Fh (x −y) = 2Fh (x) + 2Fh (y)) is a quadratic form. , Fh (tx) = tα Fh (x) for all t ≥ 0) is positively α-homogeneous. We shall easily obtain the property of convergence of minima we are looking for in the case of sequences of equicoercive Γ-converging functionals.

Kikuchi, Generating Optimal Topologies in Structural Design Using a Homogenization Method, Comp. Meth. Appl. Mech. Engrg. 197224 (1988). P. A. Soares, Topology design of structures, Nato ASI Series E, vol. 227, Kluwer, Dordrecht (1993). [9] A. L. Lions, G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland (1978). 42 G. Allaire [10] G. Buttazzo, G. Dal Maso, Integral representation and relaxation of local functionals, Nonlinear Anal. Th. Meth. Appl. 9, pp. 515-532 (1985). [11] B.

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