Isoperimetric inequalities for the first Neumann eigenvalue in Gauss space |
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Authors: | F Chiacchio G Di Blasio |
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Institution: | 1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy;2. Dipartimento di Matematica, Seconda Università degli Studi di Napoli, via Vivaldi, Caserta, Italy |
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Abstract: | We provide isoperimetric Szegö–Weinberger type inequalities for the first nontrivial Neumann eigenvalue μ1(Ω) in Gauss space, where Ω is a possibly unbounded domain of RN. Our main result consists in showing that among all sets Ω of RN symmetric about the origin, having prescribed Gaussian measure, μ1(Ω) is maximum if and only if Ω is the Euclidean ball centered at the origin. |
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Keywords: | 35B45 35P15 35J70 |
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