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We 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.

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Eigenvalue Counting Functions and Parallel Volumes for Examples of Fractal Sprays Generated by the Koch Snowflake

  • 会议论文

  • 发表日期：

    2025年

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  • Sabrina Kombrink,
  • Lucas Schmidt

摘要

We 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.