Lower bounds for nodal set of biharmonic Steklov problems

TL;DR

This paper establishes lower bounds on the measure of boundary and interior nodal sets for biharmonic Steklov eigenfunctions by proving the ellipticity of boundary operators using layer potential techniques.

Contribution

It introduces a novel approach to analyze biharmonic Steklov problems by demonstrating the ellipticity of boundary operators via layer potentials, enabling lower bound estimates.

Findings

Boundary biharmonic Steklov operators are elliptic pseudo-differential operators.

Lower bounds on boundary nodal set measure are established.

Lower bounds on interior nodal set measure are established.

Abstract

We use layer potential to establish that the boundary biharmonic Steklov operators are elliptic pseudo-differential operators. Thus we are able to establish lower bounds on both the measure of boundary nodal sets and interior nodal sets for biharmonic Steklov eigenfunctions.