| Abstract: |
| Optimization problems of the principle eigenvalue for elliptic operators of divergence form are considered. The eigen map of elliptic operator is introduced and the continuity as well as the differentiability of such a map is established. For maximization problem, the admissible control set is convexified to get the existence of optimal solutions. Whereas, for minimization problem, the relaxation of the problem under $H$-convergence is used to get a relaxed optimal solution. Some necessary conditions are presented for both problems and illustrative examples are presented as well. |
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