Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization

2012/09/24 by Carlos E. Kenig, Fanghua Lin, Kenig, Carlos E. +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.1209.5458

25 pages

arxiv created 2012/09/24 · openalex publication_date 2012/09/24 · arxiv updated 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an O(ε) estimate in H¹ for solutions with Dirichlet condition.

Citations

• Eigenvalue homogenization for quasilinear elliptic operators
• Homogenization of Green and Neumann Functions
• Eigenvalue homogenization for quasilinear elliptic equations with different boundary conditions
• Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Exact Controllability, Stabilization and Perturbations for Distributed Systems

Related

• Periodic homogenization of the principal eigenvalue of second-order elliptic operators
• First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients
• Eigenvalue homogenization for quasilinear elliptic operators in one space dimension
• First-order expansions for eigenvalues and eigenfunctions in periodic homogenization
• Lectures on Periodic Homogenization of Elliptic Systems