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

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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.
DOI : 10.4171/dm/634
Classification : 35B05, 35J05, 35P05, 35P20
Mots-clés : eigenvalues, Pleijel theorem, nodal domain, Courant's nodal domain theorem, Bessel functions 
Vladmir Bobkov. On Exact Pleijel's Constant for Some Domains. Documenta mathematica, Tome 23 (2018), pp. 799-813. doi: 10.4171/dm/634
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     author = {Vladmir Bobkov},
     title = {On {Exact} {Pleijel's} {Constant} for {Some} {Domains}},
     journal = {Documenta mathematica},
     pages = {799--813},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/634},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/634/}
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