A lower bound for the nodal sets of Steklov eigenfunctions

2014/11/03 by Wang, Xing, Zhu, Jiuyi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.0708

Abstract

We consider the lower bound of nodal sets of Steklov eigenfunctions on smooth Riemannian manifolds with boundary--the eigenfunctions of the Dirichlet-to-Neumann map. Let N_λ be its nodal set. Assume that zero is a regular value of Steklov eigenfunctions. We show that H^n-1(N_λ)≥ Cλ^(3-n)/(2) for some positive constant C depending only on the manifold.

Related

• Nodal Sets of Steklov Eigenfunctions
• Lower bounds for interior nodal sets of Steklov eigenfunctions
• Geometry and interior nodal sets of Steklov eigenfunctions
• Interior nodal sets of Steklov eigenfunctions on surfaces
• Sharp L^p estimates and size of nodal sets for generalized Steklov eigenfunctions