Lower bounds for Steklov eigenfunctions

Jeffrey Galkowski; John A. Toth

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arXiv · 2112.11415

Lower bounds for Steklov eigenfunctions

Jeffrey Galkowski·John A. Toth

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Abstract

Let $(\Omega,g)$ be a compact, analytic Riemannian manifold with 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 the author's previous work.

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Jeffrey Galkowski, John A. Toth. 2021-12-21. Lower bounds for Steklov eigenfunctions. https://arxiv.org/abs/2112.11415

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