An optimal Poincaré-Wirtinger inequality in gauss space

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

Research output: Contribution to journalArticlepeer-review

10 Citations (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.
Original languageEnglish
Pages (from-to)449-457
Number of pages9
JournalMathematical Research Letters
Volume20
Publication statusPublished - 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics

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