The hot spots conjecture on a class of domains in Rn with n ≥ 3

Peng Fei Yang

doi:10.1007/s10255-011-0112-8

The hot spots conjecture on a class of domains in Rⁿ with n ≥ 3

Peng Fei Yang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we define a class of domains in Rⁿ. 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.

Original language	English
Pages (from-to)	639-646
Number of pages	8
Journal	Acta Mathematicae Applicatae Sinica
Volume	27
Issue number	4
DOIs	https://doi.org/10.1007/s10255-011-0112-8
Publication status	Published - Oct 2011

Keywords

hot spots conjecture
Neumann eigenfunctions
reflecting Brownian motion
synchronous coupling

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10.1007/s10255-011-0112-8

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title = "The hot spots conjecture on a class of domains in Rn with n ≥ 3",

abstract = "In this paper, we define a class of domains in Rn. 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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KW - hot spots conjecture

KW - Neumann eigenfunctions

KW - reflecting Brownian motion

KW - synchronous coupling

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The hot spots conjecture on a class of domains in Rⁿ with n ≥ 3

Abstract

Keywords

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