Lower bounds for Steklov eigenfunctions

Pub Date : 2023-11-20 DOI:10.4310/pamq.2023.v19.n4.a7

Jeffrey Galkowski, John A. Toth

引用次数: 28

Abstract

Let $(\Omega,g)$ be a compact, real analytic Riemannian manifold with real analytic boundary $\partial \Omega = M$. We give $L^2$-lower bounds for Steklov eigenfunctions and their restrictions to interior hypersurfaces $H \subset \Omega^\circ$ in a geometrically defined neighborhood of $M$. Our results are optimal in the entire geometric neighborhood and complement the results on eigenfunction upper bounds in $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=3897008}{[\textrm{GT19}]}$

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Steklov特征函数的下界

设$(\Omega,g)$是一个紧实解析黎曼流形，具有实解析边界$\partial \Omega = M$。我们给出了在几何定义的$M$邻域内Steklov特征函数的$L^2$ -下界及其对内部超曲面$H \subset \Omega^\circ$的限制。我们的结果在整个几何邻域内是最优的，并且补充了特征函数上界的结果 $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=3897008}{[\textrm{GT19}]}$

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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