加权Laplace算子Dirichlet特征值问题的一个万有不等式及其应用

Abstract

Abstract: In this paper, we study the Dirichlet eigenvalue problem of the weighted Laplace operator $\mathbb {L}_\phi$ on a bounded domain $\Omega$ with a smooth boundary in $n$-dimensional Euclidean space. Under the premise that the weighted function $\phi$ satisfies certain constraints, a universal inequality of the eigenvalue problem can be obtained by using the variational method and constructing the test function appropriately.

Key words: weighted Laplace operator, Dirichlet eigenvalue problem, Green formula

CLC Number:

O186

Yang Guicheng, Wen Yangzhe, Mao Jing. A Universal Inequality for the Dirichlet Eigenvalue Problem of the Weighted Laplacian and its Application[J].Acta mathematica scientia,Series A, 2025, 45(1): 54-73.

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A Universal Inequality for the Dirichlet Eigenvalue Problem of the Weighted Laplacian and its Application

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