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2007 On the Rayleigh quotient and the first eigenvalue for some vector-valued variational problems
Friedemann Brock, R. Manásevich
Differential Integral Equations 20(4): 429-443 (2007).

Abstract

We prove that the first eigenvalue of a vector-valued $p$-Laplacian problem is equal to the first eigenvalue of the corresponding scalar $p$-Laplacian, and that the components of its first eigenvectors are merely copies of the first eigenfunction of the scalar problem. We also show variants of this result for some other homogeneous vector-valued problems.

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Friedemann Brock. R. Manásevich. "On the Rayleigh quotient and the first eigenvalue for some vector-valued variational problems." Differential Integral Equations 20 (4) 429 - 443, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35098
MathSciNet: MR2307141

Subjects:
Primary: 35J50
Secondary: 35J55 , 35J60 , 35P15 , 35P30 , 49R50

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 4 • 2007
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