Abstract. Let Ω be a smooth, convex, unbounded domain of R N. Denote by μ1(Ω) the first nontrivial Neumann eigenvalue of the Hermite operator in Ω; we prove that μ1(Ω) ≥ 1. The result is sharp since equality sign is achieved when Ω is a N-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincaré-Wirtinger inequality for functions belonging to the weighted Sobolev space H1(Ω, dγN), where γN is the N-dimensional Gaussian measure. © International Press 2013.
Brandolini B., Chiacchio F., Henrot A., Trombetti C. (2013). An optimal Poincaré-Wirtinger inequality in gauss space. MATHEMATICAL RESEARCH LETTERS, 20(3), 449-457 [10.4310/MRL.2013.v20.n3.a3].
An optimal Poincaré-Wirtinger inequality in gauss space
Brandolini B.
;
2013-01-01
Abstract
Abstract. Let Ω be a smooth, convex, unbounded domain of R N. Denote by μ1(Ω) the first nontrivial Neumann eigenvalue of the Hermite operator in Ω; we prove that μ1(Ω) ≥ 1. The result is sharp since equality sign is achieved when Ω is a N-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincaré-Wirtinger inequality for functions belonging to the weighted Sobolev space H1(Ω, dγN), where γN is the N-dimensional Gaussian measure. © International Press 2013.
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