On the nodal line of the second eigenfunction of the Laplacian over some concave domains in $\mathbb{R}^2$

Abstract

In this paper we will prove the nodal line $N$ of the second eigenfunction of the Laplacian over some simply connected concave domain $\Omega$ in $\mathbb{R}^2$ must intersect the boundary $\partial\Omega$ at exactly two points.