Casado Diaz, Juan; Garroni, Adriana Asymptotic behavior of nonlinear elliptic systems on varying domains. (English) Zbl 0952.35036 SIAM J. Math. Anal. 31, No. 3, 581-624 (2000). The following homogenization problem \(Au_n=f\) in \(\Omega_n, u_n\in W^{1,p}_0(\Omega_n,\mathbb{R}^M)\) ist studied, where \(A:W_0^{1,p}(\Omega,\mathbb{R}^M)\to W^{-1,p}(\Omega,\mathbb{R}^M)\) is a nonlinear monotone operator in divergence form. The sequence of open subsets of a bounded open set \(\Omega\) in \(\mathbb{R}^N\) is arbitrary without assumptions involving the geometry or the capacity of the closed sets \(\Omega\setminus\Omega_n.\) As additional term in the equation for the limit function \(u\) appears \(F(x,u)\mu\) where \(\mu\) is a positive Borel measure with value \(+\infty\) on large families of sets. Analogous results in the scalar case \((M=1)\) were established by G. Dal Maso and F. Murat. Reviewer: Igor I.Skrypnik (Donetsk) Cited in 21 Documents MSC: 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35B40 Asymptotic behavior of solutions to PDEs 47H05 Monotone operators and generalizations Keywords:homogenization; perforated domains; Dirichlet systems PDFBibTeX XMLCite \textit{J. Casado Diaz} and \textit{A. Garroni}, SIAM J. Math. Anal. 31, No. 3, 581--624 (2000; Zbl 0952.35036) Full Text: DOI