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

In: Optimization Methods, Theory and Applications

Author

Listed:
  • Chong Qiu

    (Soochow University, Department of Mathematics)

  • Yisheng Huang

    (Soochow University, Department of Mathematics)

  • Yuying Zhou

    (Soochow University, Department of Mathematics)

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.

Suggested Citation

  • Chong Qiu & Yisheng Huang & Yuying Zhou, 2015. "Rearrangement Optimization Problems Related to a Class of Elliptic Boundary Value Problems," Springer Books, in: Honglei Xu & Song Wang & Soon-Yi Wu (ed.), Optimization Methods, Theory and Applications, edition 127, chapter 0, pages 35-50, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-47044-2_2
    DOI: 10.1007/978-3-662-47044-2_2
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