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Homogenisation of Dirichlet problems for monotone operators in varying domains. (English) Zbl 0877.35013
Summary: We study the asymptotic behaviour, for a sequence of varying open sets \(\Omega_n\), of the solutions \(u_n\) of nonlinear Dirichlet problems for a monotone Leray-Lions operator. The method is based on the comparison between the gradient of \(u_n\) and the corrector for the \(p\)-Laplacian corresponding to the same geometry as the monotone operator. The representation of the limit problem and a corrector result are obtained.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J65 Nonlinear boundary value problems for linear elliptic equations
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