Asymptotical Analysis of Electrostatic Problems in Nonlinear Domains with Thin Perfectly Conducting Grids

In the paper we investigate the asymptotic behavior of solutions of the family of nonlinear elliptic equations in domains with thin grids concentrating near a hypersurface when the measure of wires tends to zero and the density tends to infinity. The homogenized equations and the homogenized boundary conditions are derived. The homogenization technique is based on the applying of the abstract theorem on the homogenization of the nonlinear variational functional in the Sobolev-Orlicz spaces. This theorem is proved in the paper