Uniform resolvent convergence for strip with fast oscillating boundary

Abstract

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

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Cited by in corpus (4)

• Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve
• Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model
• Scalar boundary value problems on junctions of thin rods and plates. I. Asymptotic analysis and error estimates
• Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation