Asymptotic behavior of nonlinear elliptic systems on varying domains

Abstract

We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every f ∈ W−1,p0 (Ω, RM), 1/p+ 1/p0 = 1, we study the asymptotic behavior, as h → +∞, of the solutions uh ∈ W1 0 (Ωh, RM) of the systems Auh = f in W−1,p0 (Ωh, RM), and we determine the general form of the limit problem.