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On exact Pleijel's constant for some domains

Published 12 Feb 2018 in math.AP and math.SP | (1802.04357v1)

Abstract: 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.

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Authors (1)

  1. Vladimir Bobkov 

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