球壳区域主特征值最小化问题研究  

Research on the Minimization Problem of Principal Eigenvalue in Spherical Shell Domain

作　　者：江梦萍 

机构地区：[1]浙江师范大学数学科学学院,浙江 金华

出　　处：《应用数学进展》2023年第9期3826-3833,共8页Advances in Applied Mathematics

摘　　要：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。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.

关 键 词：主特征值 最优化 球壳区域 

分 类 号：O17[理学—数学]