Upper bounds of nodal sets for eigenfunctions of eigenvalue problems

Fanghua Lin, Jiuyi Zhu

Published 2020-05-08Version 1

We aim to provide a uniform way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems in real analytic domains. The exemplary examples include biharmonic Steklov eigenvalue problems, buckling eigenvalue problems and champed-plate eigenvalue problems. The nodal sets of eigenfunctions are derived from doubling inequalities and a complex growth lemma. The novel idea is to obtain the doubling inequalities in an extended domain by a real analytic continuation and Carleman estimates.