Bobkov, Vladmir

On Exact Pleijel's Constant for Some Domains

Doc. Math. 23, 799-813 (2018)
DOI: 10.25537/dm.2018v23.799-813
Communicated by Heinz Siedentop

Summary

We provide an explicit expression for the Pleijel constant for the planar disk and some of its sectors, as well as for $N$-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.

Mathematics Subject Classification

35P05, 35P20, 35B05, 35J05

Keywords/Phrases

Pleijel theorem, eigenvalues, nodal domain, Courant's nodal domain theorem, Bessel functions

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Affiliation

Bobkov, Vladmir
Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 306 14 Plzeň, Czech Republic

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