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

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

2010-04-30

arxiv.org/abs/1004.5494v2

Mathematics

Analysis of PDEs

7 pages, 12 conference

Scientific paper

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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