Polynomial upper bound on interior Steklov nodal sets

Bogdan Georgiev; Guillaume Roy-Fortin

Polynomial upper bound on interior Steklov nodal sets

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arxiv 1704.04484 v1 pith:NXG6ZIV5 submitted 2017-04-14 math.SP math.AP

Bogdan Georgiev , Guillaume Roy-Fortin This is my paper · ORCID

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keywords nodalsetscoefficientsinteriorpolynomialsteklovupperbound

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abstract

We study solutions of uniformly elliptic PDE with Lipschitz leading coefficients and bounded lower order coefficients. We extend previous results of A. Logunov concerning nodal sets of harmonic functions and, in particular, prove polynomial upper bounds on interior nodal sets of Steklov eigenfunctions in terms of the corresponding eigenvalue $ \lambda $.

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Domains without dense Steklov nodal sets
math.AP 2019-08 accept novelty 8.0 of 10

For a dense family of analytic planar domains, Steklov eigenfunctions have fixed-size zero-free balls in the interior, so their nodal sets are not dense at any shrinking scale.

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