Geodesic
On Exact Pleijel's Constant for Some Domains
Documenta mathematica, Tome 23 (2018), pp. 799-813.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 35P05, 35P20, 35B05, 35J05
Keywords: Pleijel theorem, eigenvalues, nodal domain, Courant's nodal domain theorem, Bessel functions 
@article{DOCMA_2018__23__a38,
     author = {Bobkov, Vladmir},
     title = {On {Exact} {Pleijel's} {Constant} for {Some} {Domains}},
     journal = {Documenta mathematica},
     pages = {799--813},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a38/}
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Bobkov, Vladmir. On Exact Pleijel's Constant for Some Domains. Documenta mathematica, Tome 23 (2018), pp. 799-813. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a38/