Estimates of eigenvalues and eigenfunctions in periodic homogenization

Uniform Estimates in Two Periodic Homogenization Problems

We analyze two partial diierential equations that are posed on perforated domains. We provide a priori estimates, that do not depend on the size of the perforation: a sequence of solutions is uniformly bounded in a Sobolev space of regular functions. The rst homogeniza-tion problem concerns the Laplace-and the mean-curvature operator with Neumann boundary conditions. We derive uniform Lipschitz...

On uniform H-estimates in periodic homogenization

where the matrix a(y) = [ak`(y)] is symmetric and positive de­ nite a(y) > ¬ I with ¬ > 0. Its entries belong to L # (Y ) (Y is the cube ]0; 2 o [ N and subscript `#’ means that the space consists of Y -periodic functions). In the sequel, we will make various further length-scale regularity assumptions on the coe ̄ cients ak` which play a central role throughout the paper. Some of them are as fo...

Eigenvalues and Eigenfunctions

The article describes the eigenvalue and eigenfunction problems. Basic properties, some applications and examples in system analysis are provided.

Asymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues