Li, Liangpan On the placement of an obstacle so as to optimize the Dirichlet heat content. (English) Zbl 1491.35261 SIAM J. Math. Anal. 54, No. 3, 3275-3291 (2022). Summary: We prove that, among all doubly connected domains 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. Cited in 1 Document MSC: 35K08 Heat kernel 35B50 Maximum principles in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 49R05 Variational methods for eigenvalues of operators Keywords:heat kernel; heat content; Dirichlet boundary condition; principle of not feeling the boundary; maximum principles for parabolic equations × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] T. V. Anoop, V. Bobkov, and S. Sasi, On the strict monotonicity of the first eigenvalue of the \(p\)-Laplacian on annuli, Trans. Amer. Math. Soc., 370 (2018), pp. 7181-7199. · Zbl 1405.35064 [2] T. V. Anoop, V. Bobkov, and P. Drabek, Szego-Weinberger Type Inequalities for Symmetric Domains with Holes, preprint, arXiv:2102.05932, 2021. · Zbl 1482.35141 [3] R. Ban͂uelos, T. Kulzycki, and B. 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