Nodal Sets of Steklov Eigenfunctions near the Boundary: Inner Radius Estimates

Abstract We show that Steklov eigenfunctions in a bounded Lipschitz domain have wavelength dense nodal sets near the boundary, contrast to what can happen deep inside domain. Conversely, 2D $\Omega $, we prove any of eigenfunction contains half-ball centered at $\partial \Omega $ radius $c_{\Omega }/{\lambda }$.