Upper bounds of nodal sets for eigenfunctions of eigenvalue problems

Fanghua Lin, Jiuyi Zhu

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real analytic domains. The examples include biharmonic Steklov eigenvalue problems, buckling eigenvalue problems and champed-plate eigenvalue problems. The geometric measure of nodal sets are derived from doubling inequalities and growth estimates for eigenfunctions. It is done through analytic estimates of Morrey–Nirenberg and Carleman estimates.

Original languageEnglish (US)
JournalMathematische Annalen
DOIs
StateAccepted/In press - 2020

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Upper bounds of nodal sets for eigenfunctions of eigenvalue problems'. Together they form a unique fingerprint.

Cite this