Polynomial upper bound on interior Steklov nodal sets

  • Bogdan Georgiev

    Max Planck Institute for Mathematics, Bonn, Germany
  • Guillaume Roy-Fortin

    École de Technologie Supérieure, Montréal, Canada
Polynomial upper bound on interior Steklov nodal sets cover

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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 ([9]) 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 .

Cite this article

Bogdan Georgiev, Guillaume Roy-Fortin, Polynomial upper bound on interior Steklov nodal sets. J. Spectr. Theory 9 (2019), no. 3, pp. 897–919

DOI 10.4171/JST/266