Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization

Carlos E. Kenig; Fanghua Lin; Zhongwei Shen

Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization

Analysis of PDEs 2012-09-26 v1

Authors: Carlos E. Kenig , Fanghua Lin , Zhongwei Shen

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.

Keywords

homogenization dirichlet problem regularity for elliptic equations

Cite

@article{arxiv.1209.5458,
  title  = {Estimates of Eigenvalues and Eigenfunctions in Periodic Homogenization},
  author = {Carlos E. Kenig and Fanghua Lin and Zhongwei Shen},
  journal= {arXiv preprint arXiv:1209.5458},
  year   = {2012}
}

Comments

25 pages

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