 
Summary: Appl Math Optim 17:91102 (1988)
Applied Mathematics
and Optimization
© 1988 SpringerVerlag New York Inc.
Homogenization of Noncoercive Functionals:
Periodic Materials with Soft Inclusions
Emilio Acerbi and Danilo Percivale
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 156100 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.
I. Introduction
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 [2]).
