Lower bounds for interior nodal sets of Steklov eigenfunctions

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We study the interior nodal sets, Zλ of Steklov eigenfunctions in an n-dimensional relatively compact manifolds M with boundary and show that one has the lower bounds |Zλ|≥ cλ2-n2 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 SZ1 and SZ2, respectively.