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

Donghui Yang

arxiv: 1004.5494 · v2 · pith:R5KTRUVEnew · submitted 2010-04-30 · 🧮 math.AP

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

Donghui Yang This is my paper

classification 🧮 math.AP

keywords concaveeigenfunctionlaplacianlinemathbbnodalomegasecond

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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.

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

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