Differential and Integral Equations

A sharp lower bound for some Neumann eigenvalues of the Hermite operator

B. Brandolini, F. Chiacchio, and C. Trombetti

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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.

Article information

Source
Differential Integral Equations, Volume 26, Number 5/6 (2013), 639-654.

Dates
First available in Project Euclid: 14 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1363266082

Mathematical Reviews number (MathSciNet)
MR3086403

Zentralblatt MATH identifier
1299.74072

Subjects
Primary: 35P15: Estimation of eigenvalues, upper and lower bounds 35J70: Degenerate elliptic equations

Citation

Brandolini, B.; Chiacchio, F.; Trombetti, C. A sharp lower bound for some Neumann eigenvalues of the Hermite operator. Differential Integral Equations 26 (2013), no. 5/6, 639--654. https://projecteuclid.org/euclid.die/1363266082


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