高阶椭圆型算子组广义低阶谱的估计式  

Estimation of generalized lower-order spectrum of higher-order elliptic operators

作　　者：黄振明[1] HUANG Zhenming(Department of Mathematics and Physics,Suzhou Vocational University,Suzhou,Jiangsu 215104,China)

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《湖南城市学院学报（自然科学版）》2021年第3期50-55,共6页Journal of Hunan City University:Natural Science

摘　　要：在四阶椭圆型算子组谱的研究基础上,对高阶椭圆型算子组的广义低阶谱进行分析;依据微分算子谱理论,采用分部积分法、数学归纳法、测试函数法等技巧,获得了其估计式的主次谱间隙和两者之比的2个不等式.结果表明,随着空间维数的增加,主次谱间隙越来越小,该结论是已有文献结论的进一步推广.Based on the study of the spectrum of fourth-order elliptic operators,the generalized lower-order spectra of higher-order elliptic operators are analyzed.According to the spectrum theory of differential operator,two inequalities of the primary and secondary spectral gap and the ratio of the two are obtained by using the techniques of partial integration,mathematical induction and test function.The results show that with the increase of space dimension,the primary and secondary spectral gap becomes smaller and smaller,which is a further extension of the existing literature.

关 键 词：椭圆型算子组 低阶谱 Rayleigh-Ritz不等式 间隙估计 

分 类 号：O175.9[理学—数学]