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.
This work was supported by Natural Science Foundation of China (11471235, 11171247, 11371273) and GIP of Jiangsu Province (CXZZ13_0792).
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The authors would like to thank the referees for the valuable suggestions which have improved the early version of the manuscript.
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Qiu, C., Huang, Y., Zhou, Y. (2015). Rearrangement Optimization Problems Related to a Class of Elliptic Boundary Value Problems. In: Xu, H., Wang, S., Wu, SY. (eds) Optimization Methods, Theory and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47044-2_2
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DOI: https://doi.org/10.1007/978-3-662-47044-2_2
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