AN OPTIMAL POINCARE-WIRTINGER INEQUALITY IN GAUSS SPACE

作者：Brandolini Barbara^*; Chiacchio Francesco; Henrot Antoine; Trombetti Cristina

来源：Mathematical Research Letters, 2013, 20(3): 449-457.

DOI：10.4310/MRL.2013.v20.n3.a3

• Neumann eigenvalue
• Hermite operator
• sharp bounds

Let Omega be a smooth, convex, unbounded domain of R-N. Denote by mu(1)(Omega) the first nontrivial Neumann eigenvalue of the Hermite operator in Omega; we prove that mu(1)(Omega) %26gt;= 1. The result is sharp since equality sign is achieved when Omega is a N-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincare-Wirtinger inequality for functions belonging to the weighted Sobolev space H-1(Omega, d(gamma N)), where gamma(N) is the N-dimensional Gaussian measure.

• 出版日期2013