Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials

Estimates for Eigenvalues of Quasilinear Elliptic

In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.

Eigenvalues and Eigenfunctions

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

Homogenization of Elastic Dielectric Composites with Rapidly Oscillating Passive and Active Source Terms

This paper presents the derivation of the homogenized equations for the macroscopic response of elastic dielectric composites containing space charges (i.e., electric source terms) that oscillate rapidly at the length scale of the microstructure. The derivation is carried out in the setting of small deformations and moderate electric fields by means of a two-scale asymptotic analysis. Two types...

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...

Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating terms