A Remark on Recent Lower Bounds for Nodal Sets

DOI10.1080/03605302.2011.558556zbMath1232.58025arXiv1010.4579OpenAlexW3104646819MaRDI QIDQ3106560

Dan Mangoubi

Publication date: 28 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4579

zbMATH Keywords

Hausdorff measurelower boundnodal set

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items

Upper bounds of nodal sets for eigenfunctions of eigenvalue problems ⋮ Some remarks on nodal geometry in the smooth setting ⋮ Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions ⋮ Boundary doubling inequality and nodal sets of Robin and Neumann eigenfunctions ⋮ Geometry and interior nodal sets of Steklov eigenfunctions ⋮ Critical sets of eigenfunctions of the Laplacian ⋮ Doubling inequality and nodal sets for solutions of bi-Laplace equations ⋮ Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces

Cites Work

• Unnamed Item
• Lower bounds for nodal sets of eigenfunctions
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• Nodal sets of eigenfunctions on Riemannian manifolds
• Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators
• Local Asymmetry and the Inner Radius of Nodal Domains

This page was built for publication: A Remark on Recent Lower Bounds for Nodal Sets