JournalsdmVol. 23pp. 799–813

On Exact Pleijel's Constant for Some Domains

  • Vladmir Bobkov

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

Vladmir Bobkov, On Exact Pleijel's Constant for Some Domains. Doc. Math. 23 (2018), pp. 799–813

DOI 10.4171/DM/634