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The hot spots conjecture on a class of domains in R n with n ⩾ 3

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Abstract

In this paper, we define a class of domains in R n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains.

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Authors and Affiliations

  1. School of Science, Beijing Institute of Technology, Beijing, 100081, China

    Peng-fei Yang

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  1. Peng-fei Yang
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Correspondence to Peng-fei Yang.

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Yang, Pf. The hot spots conjecture on a class of domains in R n with n ⩾ 3. Acta Math. Appl. Sin. Engl. Ser. 27, 639–646 (2011). https://doi.org/10.1007/s10255-011-0112-8

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  • DOI: https://doi.org/10.1007/s10255-011-0112-8

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