Estimates of eigenvalues and eigenfunctions in periodic homogenization

  • Carlos E. Kenig

    University of Chicago, USA
  • Fanghua Lin

    New York University, United States
  • Zhongwei Shen

    University of Kentucky, Lexington, USA

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 \( O(\varep) \) estimate in for solutions with Dirichlet condition.

Cite this article

Carlos E. Kenig, Fanghua Lin, Zhongwei Shen, Estimates of eigenvalues and eigenfunctions in periodic homogenization. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1901–1925

DOI 10.4171/JEMS/408