Michael M. H. Pang
Abstract:
This article is a sequel to two earlier articles (one of them
written jointly with R. Banuelos) on stability results for the Neumann
eigenvalues and eigenfunctions of domains in
with
a snowflake type fractal boundary.
In particular we want our results to be applicable to the Koch snowflake
domain. In the two earlier papers we assumed that a domain
which has a snowflake type boundary
is approximated by a family of subdomains and that the Neumann heat
kernel of
and those of its approximating subdomains satisfy a
uniform bound for all sufficiently small t>0. The purpose of this
paper is to extend the results in the two earlier papers to the
situations where the approximating domains are not necessarily
subdomains of
.
We then apply our results to the Koch snowflake
domain when it is approximated from outside by a decreasing sequence of
polygons.
Submitted November 5, 2010. Published August 7, 2011.
Math Subject Classifications: 35P05, 35P15.
Key Words: Stability; approximations; Neumann eigenvalues
and eigenfunctions.
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Michael M. H. Pang Department of Mathematics, University of Missouri-Columbia Columbia, MO 65211, USA email: pangm@missouri.edu |
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