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Upper bounds of nodal sets for eigenfunctions of eigenvalue problems

Analysis of PDEs 2020-10-08 v3

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.

Keywords

Cite

@article{arxiv.2005.04079,
  title  = {Upper bounds of nodal sets for eigenfunctions of eigenvalue problems},
  author = {Fanghua Lin and Jiuyi Zhu},
  journal= {arXiv preprint arXiv:2005.04079},
  year   = {2020}
}

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Update the wording and references

R2 v1 2026-06-23T15:24:31.581Z