Lower bounds for interior nodal sets of Steklov eigenfunctions

Abstract

We study the interior nodal sets, $Z_{\lambda }$ of Steklov eigenfunctions in an $n$-dimensional relatively compact manifolds $M$ with boundary and show that one has the lower bounds $|Z_{\lambda }|\ge c{\lambda }^{\frac{2-n}{2}}$ for the size of its $(n-1)$-dimensional Hausdorff measure. The proof is based on a Dong-type identity and estimates for the gradient of Steklov eigenfunctions, similar to those in \cite{SZ1} and \cite{SZ2}, respectively.

7 pages, minor correction

References in corpus (1)

• A lower bound for the nodal sets of Steklov eigenfunctions