Isoperimetric inequalities for the first Neumann eigenvalue in Gauss space
Chiacchio, F. ; Di Blasio, G.
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012), p. 199-216 / Harvested from Numdam
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We provide isoperimetric Szegö–Weinberger type inequalities for the first nontrivial Neumann eigenvalue μ 1 (Ω) in Gauss space, where Ω is a possibly unbounded domain of ℝ N . Our main result consists in showing that among all sets Ω of ℝ N symmetric about the origin, having prescribed Gaussian measure, μ 1 (Ω) is maximum if and only if Ω is the Euclidean ball centered at the origin.

Publié le : 2012-01-01
DOI : https://doi.org/10.1016/j.anihpc.2011.10.002
Classification:  35B45,  35P15,  35J70 
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     author = {Chiacchio, F. and Di Blasio, G.},
     title = {Isoperimetric inequalities for the first Neumann eigenvalue in Gauss space},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {29},
     year = {2012},
     pages = {199-216},
     doi = {10.1016/j.anihpc.2011.10.002},
     mrnumber = {2901194},
     zbl = {1238.35072},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2012__29_2_199_0}
}

Chiacchio, F.; Di Blasio, G. Isoperimetric inequalities for the first Neumann eigenvalue in Gauss space. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) pp. 199-216. doi : 10.1016/j.anihpc.2011.10.002. http://gdmltest.u-ga.fr/item/AIHPC_2012__29_2_199_0/

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