Pleijel's theorem for a class of degenerate elliptic operators

Rupert L. Frank; Bernard Helffer

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arXiv · 2606.04951

Pleijel's theorem for a class of degenerate elliptic operators

Rupert L. Frank·Bernard Helffer

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Abstract

We prove an asymptotic upper bound on the number of nodal domains of eigenfunctions of a class of degenerate elliptic operators. Our proof yields the same constant as in Pleijel's bound for the Dirichlet Laplacian. The operators considered include the Baouendi-Grushin operator and operators with ellipticity degenerating on the boundary.

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Rupert L. Frank, Bernard Helffer. 2026-06-03. Pleijel's theorem for a class of degenerate elliptic operators. https://arxiv.org/abs/2606.04951

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