Uniform resolvent convergence for strip with fast oscillating boundary

摘要: Abstract In a planar infinite strip with fast oscillating boundary we consider an elliptic operator assuming that both the period and amplitude of oscillations are small. On impose Dirichlet, Neumann or Robin condition. all cases describe homogenized operator, establish uniform resolvent convergence perturbed to one, prove estimates for rate convergence. These results obtained as order is less, equal greater than period. It shown under homogenization type condition can change.