The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions

A. Logunov, E. Malinnikova, N. Nadirashvili +1

Let $\Omega$ be a bounded domain in ${\mathbb{R}}^n$ with $C^1$ boundary and let $u_{\lambda }$ be a Dirichlet Laplace eigenfunction in $\Omega$ with eigenvalue $\lambda$. We show that the $(n-1)$-dimensio…