ASYMPTOTIC BEHAVIOR OF NONLINEAR SYSTEMS IN VARYING DOMAINS WITH BOUNDARY CONDITIONS ON VARYING SETS

摘要

For a fixed bounded open set Ω is contained in R~N, a sequence of open sets Ω_n is contained in Ω and a sequence of sets Γ_n is contained in partial derivΩ ∩ partial derivΩ_n we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on Ω_n, satisfying Neumann boundary conditions on Γ_n and Dirichlet boundary conditions on partial derivΩ_nΓ_n. We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on Ω_n and Γ_n locally.