arXiv Open Access 2023

Small-scale mass estimates for Neumann eigenfunctions: piecewise smooth planar domains

Hans Christianson John A. Toth

Lihat Sumber

Abstrak

Let $Ω$ be a piecewise-smooth, bounded convex domain in $\R^2$ and consider $L^2$-normalized Neumann eigenfunctions $φ_λ$ with eigenvalue $λ^2$. Our main result is a small-scale {\em non-concentration} estimate: We prove that for {\em any} $x_0 \in \overlineΩ,$ (including boundary and corner points) and any $δ\in [0,1),$ $$ \| φ_λ\|_{B(x_0,λ^{-δ})\cap Ω} = O(λ^{-δ/2}).$$ The proof is a stationary vector field argument combined with a small scale induction argument.

Topik & Kata Kunci

math.AP math.SP

Penulis (2)

Hans Christianson

John A. Toth

Format Sitasi

APA MLA BibTeX

Christianson, H., Toth, J.A. (2023). Small-scale mass estimates for Neumann eigenfunctions: piecewise smooth planar domains. https://arxiv.org/abs/2309.10875

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓