Upper bounds of nodal sets for eigenfunctions of eigenvalue problems

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.

arXiv commentUpdate the wording and references

References in corpus (6)

• Lower bounds for nodal sets of eigenfunctions
• On doubling inequalities for elliptic systems
• Measure of nodal sets of analytic Steklov eigenfunctions
• Geometry and interior nodal sets of Steklov eigenfunctions
• Doubling inequality and nodal sets for solutions of bi-Laplace equations
• Nodal sets of Robin and Neumann eigenfunctions

Cited by in corpus (2)

• Kroger's upper bound types for the Dirichlet eigenvalues of the fractional Laplacian
• Doubling inequalities and critical sets of Dirichlet eigenfunctions