Variations of Constrained Domain Functionals Associated With Boundary-Value Problems
Document Type
Article
Publication Date
3-1-2001
Identifier/URL
40990517 (Pure)
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.
Repository Citation
Huang, C.,
& Miller, D.
(2001). Variations of Constrained Domain Functionals Associated With Boundary-Value Problems. Journal of Optimization Theory and Applications, 108 (3), 587-615.
https://corescholar.libraries.wright.edu/math/506
DOI
10.1023/A:1017587408883
