Variations of Constrained Domain Functionals Associated with Boundary{value Problems
نویسندگان
چکیده
We study variational formulas for maximizers for domain functionals F (x0; u (x0)), x0 2 , and R F (x; u (x)) dx over all Lipschitz domains satisfying the constraint R g (x) dx = 1. Here u is the solution of a di usion equation in . Functional variations are computed using domain variations which preserve the constraint exactly. We show that any maximizer solves a moving boundary problem for the di usion equation. We further show that, for problems with symmetry, the optimal domains are balls.
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