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Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary. (English) Zbl 1020.35011
The author studies the asymptotic behavior of a Dirichlet problem for a system of nonlinear elliptic equations in a domain with holes and zero Dirichlet condition on the boundary of holes. The convergence of the solutions in a suitable space is proved and the limit problem is characterized by capacitary methods.
MSC:
35B27Homogenization; equations in media with periodic structure (PDE)
35J55Systems of elliptic equations, boundary value problems (MSC2000)
35J60Nonlinear elliptic equations
35J65Nonlinear boundary value problems for linear elliptic equations