Nodal sets of Steklov eigenfunctions near the boundary: Inner radius estimates

Stefano Decio

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arXiv · 2102.05549

Nodal sets of Steklov eigenfunctions near the boundary: Inner radius estimates

Stefano Decio

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Abstract

We show that Steklov eigenfunctions in a bounded Lipschitz domain have wavelength dense nodal sets near the boundary, in contrast to what can happen deep inside the domain. As a converse, in a two-dimensional Lipschitz domain $\Omega$, we prove that any nodal domain of a Steklov eigenfunction contains a half-ball centered at $\partial\Omega$ of radius $c_{\Omega}/\lambda$.

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Stefano Decio. 2021-02-10. Nodal sets of Steklov eigenfunctions near the boundary: Inner radius estimates. https://arxiv.org/abs/2102.05549

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