On exact Pleijel's constant for some domains
Analysis of PDEs
2018-11-13 v1 Spectral Theory
Abstract
We provide an explicit expression for the Pleijel constant for the planar disk and some of its sectors, as well as for -dimensional rectangles. In particular, the Pleijel constant for the disk is equal to 0.4613019... Also, we characterize the Pleijel constant for some rings and annular sectors in terms of asymptotic behavior of zeros of certain cross-products of Bessel functions.
Cite
@article{arxiv.1802.04357,
title = {On exact Pleijel's constant for some domains},
author = {Vladimir Bobkov},
journal= {arXiv preprint arXiv:1802.04357},
year = {2018}
}
Comments
12 pages, 1 figure