On Pleijel's nodal domain theorem

2013/08/20 by Jean Bourgain, Bourgain, Jean
Mathematics · #35B05 #35P99 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:35B05 #msc:35P99

paper · pdf · doi:10.48550/arxiv.1308.4422

9 pages

arxiv created 2013/08/20 · arxiv updated 2013/08/22

Abstract

A slight improvement of Pleijel's estimate on the number of nodal domains is obtained, exploiting a refinement of the Faber-Krahn inequality and packing density of discs.

Related

• Pleijel nodal domain theorem in non-smooth setting
• Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions
• Discrete Nodal Domain Theorems
• Discrete Nodal Domain Theorems
• Discrete Nodal Domain Theorems