Bounds for ratios of the membrane eigenvalues

Daguang Chen; Tao Zheng

doi:10.1016/j.jde.2010.10.009

Bounds for ratios of the membrane eigenvalues

Daguang Chen^*, Tao Zheng

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

For a bounded planar region in R2, we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) [11], we can obtain better upper bound of the (k+1)-th (k≥3) membrane eigenvalues.

Original language	English
Pages (from-to)	1575-1590
Number of pages	16
Journal	Journal of Differential Equations
Volume	250
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2010.10.009
Publication status	Published - 1 Feb 2011
Externally published	Yes

Keywords

Eigenvalue
Laplace operator
Primary
Secondary
Test function

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10.1016/j.jde.2010.10.009

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title = "Bounds for ratios of the membrane eigenvalues",

abstract = "For a bounded planar region in R2, we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) [11], we can obtain better upper bound of the (k+1)-th (k≥3) membrane eigenvalues.",

keywords = "Eigenvalue, Laplace operator, Primary, Secondary, Test function",

author = "Daguang Chen and Tao Zheng",

year = "2011",

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doi = "10.1016/j.jde.2010.10.009",

language = "English",

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T1 - Bounds for ratios of the membrane eigenvalues

AU - Chen, Daguang

AU - Zheng, Tao

PY - 2011/2/1

Y1 - 2011/2/1

N2 - For a bounded planar region in R2, we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) [11], we can obtain better upper bound of the (k+1)-th (k≥3) membrane eigenvalues.

AB - For a bounded planar region in R2, we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) [11], we can obtain better upper bound of the (k+1)-th (k≥3) membrane eigenvalues.

KW - Eigenvalue

KW - Laplace operator

KW - Primary

KW - Secondary

KW - Test function

UR - http://www.scopus.com/inward/record.url?scp=78349310362&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2010.10.009

DO - 10.1016/j.jde.2010.10.009

M3 - Article

AN - SCOPUS:78349310362

SN - 0022-0396

VL - 250

SP - 1575

EP - 1590

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 3

ER -

Bounds for ratios of the membrane eigenvalues

Abstract

Keywords

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