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A unified optimality condition for eigenvalue problems. (English) Zbl 0790.49026

Summary: An optimality condition is derived for the problem of maximizing the first eigenvalue of an abstract elliptic differential operator in a Hilbert space. This condition unifies some known criteria in optimal design and gives some new ones as well. The result is obtained by using some techniques of nonsmooth optimization.

MSC:

49K27 Optimality conditions for problems in abstract spaces
49Q10 Optimization of shapes other than minimal surfaces
49J52 Nonsmooth analysis
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References:

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