Lower bounds for Steklov eigenfunctions

2021/12/21 by Galkowski, Jeffrey, Toth, John A.
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2112.11415

Abstract

Let (Ω,g) be a compact, analytic Riemannian manifold with analytic boundary ∂ Ω= M. We give L²-lower bounds for Steklov eigenfunctions and their restrictions to interior hypersurfaces H ⊂ Ω^∘ 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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