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

2021/02/10 by Decio, Stefano
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.05549

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 Ω, we prove that any nodal domain of a Steklov eigenfunction contains a half-ball centered at ∂Ω of radius c_Ω/λ.

Related

• Domains without dense Steklov nodal sets
• Interior nodal sets of Steklov eigenfunctions on surfaces
• Nodal Sets of Steklov Eigenfunctions
• Lower bounds for interior nodal sets of Steklov eigenfunctions
• Sharp L^p estimates and size of nodal sets for generalized Steklov eigenfunctions