Affiliation:
1. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Abstract
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. Conversely, in a 2D Lipschitz domain $\Omega $, we prove that any nodal domain of a Steklov eigenfunction contains a half-ball centered at $\partial \Omega $ of radius $c_{\Omega }/{\lambda }$.
Funder
Research Council of Norway
Publisher
Oxford University Press (OUP)
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