Optimization of the Principal Eigenvalue for Elliptic Operators
Optimization of the Principal Eigenvalue for Elliptic Operators
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DOI：
10.1007/s00526-021-02011-8
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Yong Jiongmin
中科院分区：
文献类型：
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作者：
Lou Hongwei;Yong Jiongmin
Maximization and minimization problems of the principle eigenvalue for divergence form second order elliptic operators with the Dirichlet boundary condition are considered. The principal eigen map of such elliptic operators is introduced and some basic properties of this map, including continuity, concavity, and differentiability with respect to the parameter in the diffusibility matrix, are established. For maximization problem, the admissible control set is convexified to get the existence of an optimal convexified relaxed solution. Whereas, for minimization problem, the relaxation of the problem under $H$-convergence is introduced to get an optimal $H$-relaxed solution for certain interesting special cases. Some necessary optimality conditions are presented for both problems and a couple of illustrative examples are presented as well..
