Some inequalities for the minimum M-eigenvalue of elasticity M-tensors

Jun He; Guangjun Xu; Yanmin Liu

doi:10.3934/jimo.2019092

Article Contents

2020, Volume 16, Issue 6: 3035-3045. Doi: 10.3934/jimo.2019092

This issue Previous Article Numerical solution to an inverse problem on a determination of places and capacities of sources in the hyperbolic systems Next Article Parametric Smith iterative algorithms for discrete Lyapunov matrix equations

Some inequalities for the minimum M-eigenvalue of elasticity M-tensors

School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, China

^* Corresponding author: Jun He
^* Corresponding author: Jun He

Received: September 30, 2018

Revised: January 31, 2019

Early access: July 2019

Published: October 2020

This work is supported by National Natural Science Foundations of China (11661084); Science and Technology Foundation of Guizhou province (Qian Ke He Ji Chu [2016]1161, [2017]1201); Innovative talent team in Guizhou Province(Qian Ke He Pingtai Rencai[2016]5619); High-level innovative talents of Guizhou Province(Zun Ke He Ren Cai[2017]8)

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Abstract

In this paper, we derive some lower bounds for the minimum M-eigenvalue of elasticity M-tensors, these bounds only depend on the elements of the elasticity M-tensors and they are easy to be verified. Comparison theorems for elasticity M-tensors are also given.

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Mathematics Subject Classification: Primary: 15A18, 15A69; Secondary: 65F15, 65F10.

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