The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains

Let Ω be a bounded domain in R^n with C^{1,1} boundary and let u_λ be a Neumann Laplace eigenfunction in Ω with eigenvalue λ. We show that the (n - 1)-dimensional Hausdorff measure of the zero set of u_λ does not exceed C\sqrtλ.