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Erschienen in:
2015 | OriginalPaper | Buchkapitel
2. Rearrangement Optimization Problems Related to a Class of Elliptic Boundary Value Problems
verfasst von : Chong Qiu, Yisheng Huang, Yuying Zhou
Erschienen in: Optimization Methods, Theory and Applications
Verlag: Springer Berlin Heidelberg
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Abstract
In this paper, we investigate two optimization problems related to a class of elliptic boundary value problems on smooth bounded domains of \(\mathbb{R}^{N}\). These optimization problems are formulated as minimum and maximum problems related to the rearrangements of given functions. Under some suitable assumptions, we show that both problems are solvable. Moreover, we obtain a representation result of the optimal solution for the minimization problem and show that this solution is unique and symmetric if the domain is a ball centered at the origin.