Isoperimetric inequalities for the first Neumann eigenvalue in Gauss space

Chiacchio, F.; Di Blasio, G.

doi:10.1016/j.anihpc.2011.10.002

Chiacchio, F. ; Di Blasio, G.

Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 199-216.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2011.10.002

Classification : 35B45, 35P15, 35J70
Mots-clés : Neumann eigenvalues, Symmetrization, Isoperimetric estimates

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     title = {Isoperimetric inequalities for the first {Neumann} eigenvalue in {Gauss} space},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {199--216},
     publisher = {Elsevier},
     volume = {29},
     number = {2},
     year = {2012},
     doi = {10.1016/j.anihpc.2011.10.002},
     mrnumber = {2901194},
     zbl = {1238.35072},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.002/}
}

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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) no. 2, pp. 199-216. doi : 10.1016/j.anihpc.2011.10.002. http://www.numdam.org/articles/10.1016/j.anihpc.2011.10.002/

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