Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 145, pp. 1-13.

Title: Stability and approximations of eigenvalues and
       eigenfunctions for the Neumann Laplacian, part I

Authors: Rodrigo Banuelos   (Purdue Univ. West Lafayette, IN, USA)
         Michael M. H. Pang (Univ. of Missouri, Columbia, MO, USA)

Abstract:
 We investigate stability and approximation properties of the lowest
 nonzero eigenvalue and corresponding eigenfunction of the Neumann Laplacian
 on domains satisfying a heat kernel bound condition.
 The results and proofs in this paper will be used and extended
 in a sequel paper to obtain stability results for domains in
 $\mathbb{R}^2$ with a snowflake type boundary.
  
Submitted February 4, 2008. Published October 24, 2008.
Math Subject Classifications: 35P05, 35P15.
Key Words: Stability; approximations; 
           Neumann eigenvalues and eigenfunctions.