Sharp bounds on the minimum $M$-eigenvalue and strong ellipticity condition of elasticity $Z$-tensors-tensors | Zendy

Chong Wang | Zendy; Gang Wang | Zendy; Lixia Liu | Zendy

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Sharp bounds on the minimum $M$-eigenvalue and strong ellipticity condition of elasticity $Z$-tensors-tensors

Author(s) -

Chong Wang,

Gang Wang,

Lixia Liu

Publication year - 2021

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2021205

Subject(s) - eigenvalues and eigenvectors , elasticity (physics) , mathematics , upper and lower bounds , mathematical analysis , combinatorics , physics , quantum mechanics , thermodynamics

In this paper, we establish sharp upper and lower bounds on the minimum M -eigenvalue via the extreme eigenvalue of the symmetric matrices extracted from elasticity Z -tensors without irreducible conditions. Based on the lower bound estimations for the minimum M -eigenvalue, we provide some checkable sufficient or necessary conditions for the strong ellipticity condition. Numerical examples are given to demonstrate the proposed results.

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