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Journal Article

Polynomial upper bound on interior Steklov nodal sets

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Georgiev,  Bogdan
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4171/JST/266
(Publisher version)

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Citation

Georgiev, B., & Roy-Fortin, G. (2019). Polynomial upper bound on interior Steklov nodal sets. Journal of Spectral Theory, 9(3), 897-919. doi:10.4171/JST/266.


Cite as: https://hdl.handle.net/21.11116/0000-0004-F98C-6
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 $