Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake

Abstract

We apply recent results by the authors to obtain bounds on remainder terms of the Dirichlet Laplace eigenvalue counting function for domains that can be realised as countable disjoint unions of scaled Koch snowflakes. Moreover we compare the resulting exponents to the exponents in the asymptotic expansion of the domain's inner parallel volume.

Added details, fixed typos. 15 pages, 10 figures