Abstract
We prove that, for any convex planar set
, the first non-trivial
Neumann eigenvalue
of the Hermite operator is greater than or equal to 1. Furthermore, under some additional
assumptions on ,
we show that
if and only if
is any strip. The study of the equality case requires, among other things, an
asymptotic analysis of the Neumann eigenvalues of the Hermite operator in thin
domains.