On the nodal line of a second eigenfunction of the Laplacian-Dirichlet in some annular domains with dihedral symmetry

Acushla Sarswat

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arXiv · 1411.0221

On the nodal line of a second eigenfunction of the Laplacian-Dirichlet in some annular domains with dihedral symmetry

Acushla Sarswat

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Abstract

Let $Ω$ be a bounded annular $C^{1,1}$ domain in $\mathbb{R}^2$ which is left invariant under the action of the dihedral group $D_n$ of isometries of $\mathbb{R}^2$ .We show that the nodal line of a second Dirichlet eigenfunction must intersect the boundary of $Ω$, under suitable conditions on $\frac{\partial}{\partial θ}$ .

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Acushla Sarswat. 2014-11-02. On the nodal line of a second eigenfunction of the Laplacian-Dirichlet in some annular domains with dihedral symmetry. https://arxiv.org/abs/1411.0221

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