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

Donghui Yang

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arXiv · 1004.5494

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

Donghui Yang

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Abstract

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

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Donghui Yang. 2010-06-10. On the nodal line of the second eigenfunction of the Laplacian over some concave domains in $\mathbb{R}^2$. https://arxiv.org/abs/1004.5494

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