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28 March 2024
 
  » arxiv » 1209.6275

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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
AbstractThis 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
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