Variations of Constrained Domain Functionals Associated with Boundary-Value Problems

C. Huang and D. Miller
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C. Huang: Wright State University
D. Miller: Wright State University

Journal of Optimization Theory and Applications, 2001, vol. 108, issue 3, No 7, 587-615

Abstract: Abstract We study variational formulas for maximizers for domain functionalsF(x0, u(x0)), x0∈Ώ, and ∫ΏF(x,u(x))dxover all Lipschitz domains Ώ satisfying the constraint∫Ώg(x) dx=1. Here, u is the solution ofa diffusion equation in Ώ. Functional variations arecomputed using domain variations which preserve the constraint exactly. Weshow that any maximizer solves a moving boundary problem for the diffusionequation. Further, we show that, for problems with symmetry, the optimaldomains Ώ are balls.

Keywords: Domain functionals; boundary-value problems; domain variations; shape optimization (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017587408883

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