Summary: Appl Math Optim 17:91-102 (1988)
© 1988 Springer-Verlag New York Inc.
Homogenization of Noncoercive Functionals:
Periodic Materials with Soft Inclusions
Emilio Acerbi and Danilo Percivale
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 1-56100 Pisa, Italy
Communicated by D. Kinderlehrer
Abstract. In this paper we study the asymptotic behavior, as h-> oo, of the
minimum points of the functionals
f [f(hx, Du)+gu] dx,
where f(x, #) is periodic in xand convex in ~:, and u is vector valued. A
convergence theorem is stated without uniform coerciveness assumptions.
The classical homogenization problem is the study of the behavior, as h ~ ~, of
the minimum points on Uo+W~"pof the functionals
f [f(hx, Du)+gu] dx, (1.1)
where f(x, #) is periodic in x and convex in ~:. Many convergence results have
been obtained in the scalar case u: 12~ R (see the extensive bibliography of ).