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A sharp lower bound for some Neumann eigenvalues of the Hermite operator | B. Brandolini
; F. Chiacchio
; C. Trombetti
; | Date: |
27 Sep 2012 | Abstract: | This paper deals with the Neumann eigenvalue problem for the Hermite operator
defined in a convex, possibly unbounded, planar domain $Omega$, having one
axis of symmetry passing through the origin. We prove a sharp lower bound for
the first eigenvalue $mu_1^{odd}(Omega)$ with an associated eigenfunction odd
with respect to the axis of symmetry. Such an estimate involves the first
eigenvalue of the corresponding one-dimensional problem. As an immediate
consequence, in the class of domains for which
$mu_1(Omega)=mu_1^{odd}(Omega)$, we get an explicit lower bound for the
difference between $mu(Omega)$ and the first Neumann eigenvalue of any strip. | Source: | arXiv, 1209.6275 | Services: | Forum | Review | PDF | Favorites |
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