Journal of Convex Analysis 09 (2002), No. 1, 269--286
Copyright Heldermann Verlag 2002
An Elementary Derivation of the Generalized Kohn-Strang Relaxation Formulae
Kewei Zhang
School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, Great Britain
k.zhang@sussex.ac.uk
We give elementary proofs of the quasiconvex relaxation for the generalized Kohn-Strang functions [see G. Allaire and G. Francfort, Anal. Non-Lin. H. Poincare Inst. 15 (1998) 301--339; G. Allaire and V. Lods, Proc. Royal Soc. Edin. 129A (1999) 439--466] originally studied in an optimal design problem [R. V. Kohn and D. Strang, Comm. Pure Appl. Math. 39 (1986) 113--137, 139--183, 353--377]. We show that by using the translation method, we can recover the relaxations without using the homogenization method and the G-closure theory as in the papers of Allaire [loc. cit.]. Our calculations give further geometric insight of the relaxation and connections to other related areas.
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