一类偏微分算子组广义次谱的显式上界  

Explicit Upper Bound of Generalized Second Spectrum for a System of Partial Differential Operator

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

机构地区：[1]苏州市职业大学数理部

出　　处：《武夷学院学报》2019年第6期43-46,共4页Journal of Wuyi University

摘　　要：借助微分算子谱理论,对一类偏微分算子组低阶离散谱进行估计,利用Laplace算子的运算性质、分部积分、测试函数、Rayleigh定理和Schwarz不等式等技巧,发现这类算子组主谱与其相应特征向量之间存在的不等式关系,证明所选择的测试函数与主谱、空间维数间的关系,最终获得用主谱来估计次谱上界的一个显式不等式,结果显示其界仅与空间维数有关,而与区域的几何度量无关,其结论是参考文献结论的进一步推广。In this paper,estimate of lower-order discrete spectra for a system of partial differential operator is considered by spectral theory of differential operators.The relationship between the principal spectrum and its corresponding eigenvector is found.The relationship among the selected trial functions,the principal spectrum and the space dimension is proved.The techniques are to use the operational property of Laplacian operator,integration by parts,trial function,Rayleigh theorem and Schwarz inequality etc.The explicit inequality estimating the upper bound of the second spectrum in terms of principal one is obtained at last.The result shows this bound is only dependent on the space dimension,but does not depend on the measure of the domain in which the problem is concerned.The results in bibliography are expanded in this paper.

关 键 词：偏微分算子组 广义次谱 变分法 特征向量 显式上界 

分 类 号：O175.4[理学—数学]