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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