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球壳区域主特征值最小化问题研究
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Abstract:
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.
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