In a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of th eoscillations 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.
Uniform resolvent convergence for strip with fast oscillating boundary
FAELLA, Luisa;
2013-01-01
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 th eoscillations 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
