Rearrangement Optimization Problems Related to a Class of Elliptic Boundary Value Problems

Chong Qiu, Yisheng Huang and Yuying Zhou ()
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Chong Qiu: Soochow University, Department of Mathematics
Yisheng Huang: Soochow University, Department of Mathematics
Yuying Zhou: Soochow University, Department of Mathematics

Chapter Chapter 2 in Optimization Methods, Theory and Applications, 2015, pp 35-50 from Springer

Abstract: Abstract In this paper, we investigate two optimization problems related to a class of elliptic boundary value problems on smooth bounded domains of ℝ N $$\mathbb{R}^{N}$$ . 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.

Keywords: Existence and uniqueness; Optimization; Eigenvalue; Rearrangements (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-47044-2_2

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DOI: 10.1007/978-3-662-47044-2_2

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