On the inner radius of the nonvanishing set for eigenfunctions of complex elliptic operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914386250039296 |
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| author | Ueberschaer, Henrik Friedland, Omer |
| author_facet | Ueberschaer, Henrik Friedland, Omer |
| contents | Let $Ω\subset\mathbb{R}^d$ be any open set. We consider solutions of $Hψ_λ=λψ_λ$, $λ\in\mathbb{C}$, where $H$ is an $m$th order complex constant-coefficient elliptic partial differential operator. We prove that either the eigenfunctions satisfy a lower bound on the inner radius of the complement of the zero set of $ψ_λ$ in $Ω$ of order $|λ|^{-1/m}$, or 100% of the $L^2$ mass of $ψ_λ$ concentrates in a boundary layer of width $|λ|^{-1/m}$, as $|λ|\to+\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the inner radius of the nonvanishing set for eigenfunctions of complex elliptic operators Ueberschaer, Henrik Friedland, Omer Analysis of PDEs Let $Ω\subset\mathbb{R}^d$ be any open set. We consider solutions of $Hψ_λ=λψ_λ$, $λ\in\mathbb{C}$, where $H$ is an $m$th order complex constant-coefficient elliptic partial differential operator. We prove that either the eigenfunctions satisfy a lower bound on the inner radius of the complement of the zero set of $ψ_λ$ in $Ω$ of order $|λ|^{-1/m}$, or 100% of the $L^2$ mass of $ψ_λ$ concentrates in a boundary layer of width $|λ|^{-1/m}$, as $|λ|\to+\infty$. |
| title | On the inner radius of the nonvanishing set for eigenfunctions of complex elliptic operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.10602 |