ASYMPTOTIC BEHAVIOR OF NONLINEAR ELLIPTIC SYSTEMS ON VARYING DOMAINS.

We consider a monotone operator of the form Au = -div(a(x, Du)), with Ω ⊆ Rn and a : Ω x MM x N → MM x N, acting on W1, p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every ƒ ∈ W-1, p′ (Ω, RM), 1/p+1/p′ = 1, we study the asymptotic behavior, as h !→ +&infini;, of the solutions uh ∈ W¹ 0 (Ωh, RM) of the systems Auh = ƒ in W-1, p′ (Ωh, RM), and we determine the general form of the limit problem. [ABSTRACT FROM AUTHOR]