On the placement of an obstacle so as to optimize the Dirichlet heat content
Abstract
We prove that among all doubly connected domains of Rn (n>=2) bounded by two spheres of given radii, the Dirichlet heat content at any fixed time achieves its minimum when the spheres are concentric. This is shown to be a special case of a more general theorem concerning the optimal placement of a convex obstacle inside some larger domain so as to maximize or minimize the Dirichlet heat content.
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