An optimal Poincaré-Wirtinger inequality in gauss space

Barbara Brandolini; Barbara Brandolini; Francesco Chiacchio; Cristina Trombetti; Antoine Henrot

An optimal Poincaré-Wirtinger inequality in gauss space

Barbara Brandolini, Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti, Antoine Henrot

Matematica e Informatica

Risultato della ricerca: Article › peer review

10 Citazioni (Scopus)

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.

Lingua originale	English
pagine (da-a)	449-457
Numero di pagine	9
Rivista	Mathematical Research Letters
Volume	20
Stato di pubblicazione	Published - 2013

All Science Journal Classification (ASJC) codes

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title = "An optimal Poincar{\'e}-Wirtinger inequality in gauss space",

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 Poincar{\'e}-Wirtinger inequality for functions belonging to the weighted Sobolev space H1(Ω, dγN), where γN is the N-dimensional Gaussian measure. {\textcopyright} International Press 2013.",

author = "Barbara Brandolini and Barbara Brandolini and Francesco Chiacchio and Cristina Trombetti and Antoine Henrot",

year = "2013",

language = "English",

volume = "20",

pages = "449--457",

journal = "Mathematical Research Letters",

issn = "1073-2780",

publisher = "International Press of Boston, Inc.",

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T1 - An optimal Poincaré-Wirtinger inequality in gauss space

AU - Brandolini, Barbara

AU - Chiacchio, Francesco

AU - Trombetti, Cristina

AU - Henrot, Antoine

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/494009

M3 - Article

VL - 20

SP - 449

EP - 457

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

ER -