English

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

Spectral Theory 2021-06-24 v1

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.

Keywords

Cite

@article{arxiv.2106.12480,
  title  = {On the placement of an obstacle so as to optimize the Dirichlet heat content},
  author = {Liangpan Li},
  journal= {arXiv preprint arXiv:2106.12480},
  year   = {2021}
}