Quantitative analysis of generalized second spectrum for a class of multiple Laplace operators
In this paper,we study the lower order spectrum of a class of arbitrary multiple Laplace operators in the bounded region of Rm (m ≥ 2).By using Sturm Liouville theory,partial integral method,mathematical induction method and Schwarz inequality,we prove the inequality between the main spectrum and its characteristic function,and obtain the explicit upper bound inequality for estimating the generalized subspectrum by the main spectrum.The upper bound of the estimation is related to the order of the operator and the dimension of the space,but not to the geometric measure of the region in question.The conclusion is a further extension of that of Coster and Nicaise,which has a cer tain reference value in the study of the theory of partial differential operators.
Multiple Laplace operatorGeneralized lower order spectraRayleigh theoremYoung inequalityUpper bound estimation
NETL
NSTL
万方数据
维普
