The location of the hot spot in a grounded convex conductor

DOI10.1512/IUMJ.2011.60.4578zbMath1328.35063arXiv1012.4742OpenAlexW2963249292MaRDI QIDQ2898368

Rolando Magnanini, Lorenzo Brasco, Paolo Salani

Publication date: 11 July 2012

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4742

zbMATH Keywords

heat equationeigenfunctionshot spotSantalo point

Mathematics Subject Classification ID

Heat equation (35K05) Maximum principles in context of PDEs (35B50) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

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Movement of centers with respect to various potentials ⋮ The location of hot spots and other extremal points ⋮ Geometric estimation of a potential and cone conditions of a body ⋮ Nearly optimal stability for Serrin's problem and the soap bubble theorem ⋮ Short-time behavior for game-theoretic \(p\)-caloric functions ⋮ Uniqueness of the critical point for solutions of some \(p\)-Laplace equations in the plane ⋮ Experimental investigation on the uniqueness of a center of a body ⋮ Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators ⋮ Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities ⋮ On maximizing the fundamental frequency of the complement of an obstacle ⋮ On the Placement of an Obstacle So As to Optimize the Dirichlet Heat Trace ⋮ On the stability for Alexandrov's soap bubble theorem ⋮ Localisation of the first eigenfunction of a convex domain

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