Electron. J. Diff. Eqns., Vol. 2008(2008), No. 145, pp. 1-13.

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

Rodrigo Bañuelos, Michael M. H. Pang

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.

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  Rodrigo Bañuelos
Department of Mathematics, Purdue University
West Lafayette, IN 47906, USA
email: banuelos@math.purdue.edu
Michael M. H. Pang
Department of Mathematics, University of Missouri
Columbia, MO 65211, USA
email: pangm@math.missouri.edu

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