%0 Journal Article
%T 球壳区域主特征值最小化问题研究<br>Research on the Minimization Problem of Principal Eigenvalue in Spherical Shell Domain
%A 江梦萍
%J Advances in Applied Mathematics
%P 3826-3833
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.129376
%X 本文主要考虑Neumann边界条件下Laplace算子的不定权主特征值问题。在权函数为变号且有界的限制下，我们研究了球壳区域内的主特征值最小化问题，证明了其存在性和权函数的bang-bang分布。这些结果在生物种群资源和优化问题中有重要应用。<br />
In this paper, we mainly consider the principal eigenvalue problem of Laplace operator with indefi-nite weights under Neumann boundary condition. The existence and bang-bang distribution of the minimization of the principal eigenvalue in the spherical shell region are proved under the con-straint that weight function is sign-changing and bounded. These results have important applica-tions in biological population resources and optimization problems.
%K 主特征值，最优化，球壳区域<br>Principal Eigenvalue
%K Optimization
%K Spherical Shell Domain
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=71881