Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization

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 $O(\epsilon )$ estimate in $H^1$ for solutions with Dirichlet condition.

25 pages

References in corpus (7)

• Convergence Rates in L^2 for Elliptic Homogenization Problems
• Interior error estimate for periodic homogenization
• Eigenvalue homogenization for quasilinear elliptic operators
• Homogenization of Green and Neumann Functions
• Eigenvalue homogenization for quasilinear elliptic equations with different boundary conditions
• Eigenvalue homogenization for quasilinear elliptic operators in one space dimension
• Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian