On the placement of an obstacle so as to optimize the Dirichlet heat content

Liangpan Li

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arXiv · 2106.12480

On the placement of an obstacle so as to optimize the Dirichlet heat content

Liangpan Li

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Abstract

We prove that among all doubly connected domains of R^n (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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Liangpan Li. 2021-06-23. On the placement of an obstacle so as to optimize the Dirichlet heat content. https://arxiv.org/abs/2106.12480

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