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• W2893582139 abstract "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." @default.
• W2893582139 created "2018-10-05" @default.
• W2893582139 creator A5016246712 @default.
• W2893582139 creator A5060593522 @default.
• W2893582139 date "2018-09-29" @default.
• W2893582139 modified "2023-09-27" @default.
• W2893582139 title "Optimization of the Principal Eigenvalue for Elliptic Operators" @default.
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• W2893582139 doi "https://doi.org/10.48550/arxiv.1810.00152" @default.
• W2893582139 hasPublicationYear "2018" @default.
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