# Polynomial upper bound on interior Steklov nodal sets

## TL;DR

This paper establishes polynomial upper bounds on the interior nodal sets of Steklov eigenfunctions, extending previous harmonic function results to more general elliptic PDEs with Lipschitz coefficients.

## Contribution

It extends Logunov's results on harmonic functions to elliptic PDEs with Lipschitz coefficients, providing polynomial bounds on Steklov eigenfunction nodal sets.

## Key findings

- Polynomial upper bounds on interior Steklov nodal sets in terms of eigenvalue λ
- Extension of harmonic function nodal set results to elliptic PDEs with Lipschitz coefficients
- Generalization of previous bounds to broader class of elliptic PDEs

## Abstract

We study solutions of uniformly elliptic PDE with Lipschitz leading coefficients and bounded lower order coefficients. We extend previous results of A. Logunov concerning nodal sets of harmonic functions and, in particular, prove polynomial upper bounds on interior nodal sets of Steklov eigenfunctions in terms of the corresponding eigenvalue $ \lambda $.